Could i still have an infection in my tonsils if my doctor didn't see it, ran out of antibiotics and felt pain in my throat but he didn't see it?

Absolutely: You can have 'deep' infection which is not visible but can recur (as an abscess)...Finish the antibiotics!

Yes: Sore throat treated with antibiotics should heal, but it is possible to have an infection that doesn't respond to routine antibiotics. It is also possible that you have a virus that is unaffected by the medications. Just give it time and things should improve.