Should I get another credit card?

so i am currently a college student with one credit card and one debit card, both in my name. my dad cosigned for my credit card and he pays the bill. the credit card is used for living necessities like groceries and what not. the debit card is all my personal money from working and i use it for extracurricular expenses. would it be a better idea to get a 2nd credit card to replace the use of my debit card and then just cut a check myself for that bill?
basically, would paying off two credit cards on a monthly basis help build my credit much more than just one? idk how all this shite works. TIA