Right Bunsey lets get this clear. IT IS NOT YOUR FAULT...yes I am shouting at you. You love your hammies and always do what is right for them. We are giving meds at the moment so here is our tip. You need to get your mum or dad to help you. Get one of your dads big old hankies and wrap it round the hamster like a shawl. Let him bite at the cloth and then while you are holding him (you need to draw up the right dosage first) get your mum to push the syringe into the side of his mouth and squish it in. They are usually too busy biting the hankey to notice
You should give him some Vetark pro C in his water. Sorry but you may have to go to P@H to get it and hopefully this will keep his bowel working well. I doubt he swalloed all the Baytril and likely spat it out anyway so don't fret. It is easy once you get the knack but you do need two pairs of hands. Keep us posted and ask for further help. If you want I will do a photo guide for you.