Great advice has already been given.
I, too, have had to administer medicine by myself with my child, so I've had to lay him down and put his arms by his side and sort of sit over him (no weight on him, of course) and hold his arms down by his side with my legs. He's pinned down. It sounds awful. It's not pleasant for anyone. It's surely not his first lesson in learning he must do what his mother says. And if he would take his medicine sitting up like his mother said, it never would go to the pin down on the floor. None of this is done in frustration, though you will surely not enjoy it and might get frustrated with having to administer medicine. I really wish you the best of luck.
The cheek squeeze, as it was referred to, if it's what I did, it means you put the sringe into your sons cheek and then squeeze a little bit at a time. let him swallow. Squeeze a little more and continue this process until medicine is down. giving a small bit into the cheek at a time is mostly so that he won't spit it out or that if he does, you don't lose much.
Giving medicine can be a bad experience for everyone if child thinks it's an option to refuse it.
Whatever you do, do your best to make sure that your child swallows ALL of the prescribed medicine and that only the smallest amounts are being lost. As I'm sure you know, it's important that your child get the full prescription of the antibiotic.
Oh, and my kids have had amoxicillin many times, and it's worked well enough for us. We've never had to follow through with another medication afterwards, though I have heard of that. Just so you know, there is hope that this amoxicillin will do the job.