Need help in designing a database with a need of adding new columns or tables dynamically
You have the wrong table structure planned.

Tip: Naming a series of columns on a table with a sequential number (foobar1, foobar2, foobar3) is often a sign of incorrect database design. 

Many-To-Many

You have children and you have vaccines as entities. Each should be represented by a table.

Furthermore, you have a relationship between those two entities. Each child can get a dose of zero, one, or more vaccines. Each vaccine may be given to zero, one, or more children. That means these two entities have a Many-To-Many relationship. 

A Many-To-Many relationship is always a problem. The solution is always a third table that bridges the other two tables, representing the relationship between them. The bridging table always has at least two fields; as a child table, it has a foreign key to each of the parent tables. 

In your case, the bridging table would be named something like dose, tracking which kid got a dose of which vaccine. And in your case, the table would have a third field, the date when the dose was given.



To present this data together, you perform a database join to extract various columns from the various tables where rows match up the foreign key on the child table (dosage) to the primary key of each the parent tables (patient &amp; vaccine).



For more discussion of Many-To-Many, search for the canonical example: Books, Authors, and a bridging table named something like Authorship.  Another example is employees being assigned to teams/projects. Yet another example is music albums where an album is categorized one or more genres, and each genre can have many albums assigned to it, as discussed in this Question.

Also search to learn more about how to separate such data into tables, a process known as database normalization.


  Each child will have his own schedule and history of administered dates.


This Answer addresses only the “history of administered dates” portion of your problem, not the scheduling.


  This is my first project using databases. 


Your problem of vaccination records is not simple. As a beginner, I suggest working on a simpler problem.