mysql change password in session
According to MySQL Documentation on SET PASSWORD

The SET PASSWORD statement assigns a password to an existing MySQL
user account.   If the password is specified using the PASSWORD() or
OLD_PASSWORD() function, the literal text of the password should be
given. If the password is specified without using either function, the
password should be the already-encrypted password value as returned by
PASSWORD().
With no FOR clause, this statement sets the password for the current
user. Any client that has connected to the server using a nonanonymous
account can change the password for that account

However, you just been struck by lightning because the same webpage says

Important
SET PASSWORD may be recorded in server logs or in a history file such as ~/.mysql_history, which means that plaintext passwords may be
read by anyone having read access to that information. See Section
6.1.2, “Password Security in MySQL”.
Note
If you are connecting to a MySQL 4.1 or later server using a pre-4.1 client program, do not use the preceding SET PASSWORD or
UPDATE statement without reading Section 6.1.2.3, “Password Hashing in
MySQL”, first. The password format changed in MySQL 4.1, and under
certain circumstances it is possible that if you change your password,
you might not be able to connect to the server afterward.

Your password change is forever, so to speak.
HOW TO FIX IT
Suppose your user is myuser@localhost, you can have someone with ALL PRIVILEGES run this
UPDATE mysql.user SET password=OLD_PASSWORD('[your password]')
WHERE user='myuser' AND host='localhost';
FLUSH PRIVILEGES;

If you have no DBA but can restart mysql, then do this
service mysql restart --skip-networking --skip-grant-tables
mysql -e&quot;UPDATE mysql.user SET password=OLD_PASSWORD('[your password]') WHERE user='myuser' AND host='localhost'&quot;
service mysql restart