Okay please don't take this the wrong way but as someone who is actually allergic to an antibiotic, I have to say I don't really like the idea of you lying about having an allergy when you don't.

There are a lot of reasons why he might not have given you amoxicillin. A lot of people have, or develop allergies to it. It happened to me. I could take amoxicillin when I was very young, but as I got older I started having allergic reactions to penicillin and penicillin derivatives.
Also, antibiotic resistant bacteria is on the rise and since penicillin is the oldest antibiotic alot of bugs are resistant to it, so that might have been his motive for not giving it to you.