Account creation and log-in system
Welcome to code review, and good job for your first program I suppose.

Style


Docstrings: Python documentation strings (or docstrings) provide a convenient way of associating documentation with Python modules,
functions, classes, and methods. As you can see, even for a
relatively simple function, documenting using comments quickly makes
it unpleasant and difficult to read. So, to solve this, the docstring
was introduced. You should include docstrings to the functions you
created indicating what they return and some type hints if necessary.

def app(user_name): 
    """Print user name."""

def create():
    """Create new account."""

Descriptive variable names: The name app(user_name) can be changed to print_username() since it's a good practice to create
descriptive variable names which improve readability for you and for 
other people using your code. Same goes for create() that can be
create_account()
PEP0008 The official Python style guide https://www.python.org/dev/peps/pep-0008/ I suggest you check this, will help you write more pythonic code.
Blank lines: Your functions contain many blank lines and according to PEP0008 you should use blank lines sparingly:
Surround top-level function and class definitions with two blank
lines. Method definitions inside a class are surrounded by a single
blank line. Extra blank lines may be used (sparingly) to separate
groups of related functions. Blank lines may be omitted between a
bunch of related one-liners (e.g. a set of dummy implementations).


Code

The code is a bit long and can be shortened. Storing all usernames and passwords and everything else in the same file I think is a bad idea and is very unreliable because all things would be mixed up and you don't know which is what, I suggest you create a .txt file for each user and make the file name same as the user name so the program checks the folder and if the user is not found, it prompts the user accordingly.  And still this is not the best way to do it however it is better than mixing all things up. 

exists = os.path.exists("C:/Users/Tom/Desktop/test/login_project/account_info.txt")


this line should be cleaned up or replaced by input() (If i'm using your code it's very obvious that the path will not exist and the condition if not exists: will always evaluate to True.

info_list = [user_name, password, email]


The variable user_name is referenced before assignment, you should define your variables at the top of the function body to avoid such problems.

unused variable(line 103) you should clean such things up upon completion.

main_choice = ""


Bug: 
This appears after creating a new account and trying to login.
 - Error: [0] account(s) found in database 

These are unecessary variables: 

creating_username = True
creating_password = True


followed by while creating_username: and while_creating_password:

which can be written:

while True:
    # block


and same goes to entering_info = True and main_choosing = True in other functions.

else:
    creating_username = False


can be replaced with break in the following way:

else:
    break


instead of manually closing the file you just opened, you may use with &amp; as context managers that automatically carry the opening and closing activities for you in the following way and the file will be closed automatically.

f = open("account_info.txt", "a+")
f.write(f"{info_list}\r\n")
f.close()


can be written:

with open('account_info.txt', 'a+') as data:
    # do things


line 69: the file was opened twice (I think you forgot to clean this up)

f = open("account_info.txt", "r")

file_contents = f.read()

f = open("account_info.txt", "r")
list_ = [char for char in f.readlines() if char != "\n"]


Descriptive variable names: I think this is the second time I mention this: a code is designed to be interpreted by machines and to be read and understood by human beings, try as much as you can to avoid ambiguous variable/method/function names.

for i in list_:
for y in list_:
counter_one = 1
counter_two = 1


what is i? what is y? what is counter_one what does it count? what is counter_two?

print("\nWelcome.\n")
choosing()


if __name__ == '__main__': guard to be used at the end of your script, allows your module to be imported by other modules without running the whole script.

This should be placed at the end of your script like the following:

if __name__ == '__main__':
    print('\nWelcome.\n')
    choosing()


I tried to simplify your program and here's what I came up with (And still this is not the proper way to do it in the real world, it's just for the sake of the example) and you might modify it if you want it to keep running and keep asking for input or whatever structure you want, you might consider this as an assignment:

import os


def create_account(path):
    """Create and save username to a Usernames folder."""
    if 'Usernames' not in os.listdir(path):
        os.mkdir('Usernames')
    os.chdir('Usernames')
    new_username = input('Enter new user name: ')
    if new_username + '.txt' in os.listdir(path + 'Usernames'):
        raise ValueError(f'Username {new_username} already exists.')
    new_password = input('Enter new password: ')
    confirm_pass = input('Confirm password: ')
    while new_password != confirm_pass:
        print('Passwords do not match!')
        new_password = input('Enter new password: ')
        confirm_pass = input('Confirm password: ')
    with open(new_username + '.txt', 'w') as new_user:
        new_user.write(new_username + ' ')
        new_user.write(new_password)
    print(f'Account created successfully.')


def login(path):
    """Login using user name and password."""
    if 'Usernames' in os.listdir(path):
        os.chdir('Usernames')
        username = input('Enter Username or q to quit: ')
        while username + '.txt' not in os.listdir(path + 'Usernames') and username != 'q':
            print(f'Username {username} does not exist.')
            username = input('Enter Username or q to quit: ')
        if username == 'q':
            exit(0)
        password = input('Enter password: ')
        if username + '.txt' in os.listdir(path + 'Usernames'):
            user, valid_pass = open(username + '.txt').read().rstrip().split()
            while password != valid_pass:
                print('Invalid password.')
                password = input('Enter password: ')
            print('Login successful.')
    else:
        print('Database not found!')
        exit(1)


def start_login(path):
    """Run login interactively."""
    print('Welcome to my program.')
    user_mode = input('Enter L for login or C for creating a new account or Q to exit.').lower()
    while user_mode not in 'lcq':
        print('Invalid command')
        user_mode = input('Enter L for login or C for creating a new account or Q to exit.').lower()
    if user_mode == 'l':
        login(path)
    if user_mode == 'c':
        create_account(path)
    if user_mode == 'q':
        print('Thank you for using my program')
        exit(0)


if __name__ == '__main__':
    database_path = input('Enter database path: ').rstrip()
    while not os.path.exists(database_path):
        print('Invalid path')
        database_path = input('Enter database path: ').rstrip()
    start_login(database_path)