Hi Jay
It sounds like he's just biting because his wound is hurting so don't feel bad. It's probably most important to give him the baytril by mouth so it's great that you're managing this. You might have to brace yourself for his being a bit grumpy. I always find the little ones are very forgiving.
Sorry this is so tough for you and Cookie. You're doing your best. If it were my hammy I would try to keep the cage very clean and soft, focus on giving him the baytril, as a priority, and attempt to clean the wound when I was a bit more relaxed. Perhaps, if you're holding Cookie, someone in your family might be less nervous and be able to gently clean the wound? The swaddling method is very good (we've had to use this for our poorly bunnies
) For buns we've heard this called the bunny burrito! So I guess this would be a hammy burrito
I also imagine it's important that this course of baytril lasts long enough to allow the wound to heal. If his tummy still seems bad a day or two before the antibiotics are due to run out, call the vet for more advice.
If you can't get him to take the antibiotics you may find he'll eat it, as Dora said, mixed with some tasty food. I'm a bit wary about advising what food but I'll bet other forum users have plenty of ideas for you.
Best of luck Jay, thinking of you both x