It sounds as if she needs to be seen again. If the eye is continuing to swell it could rupture and this sort of eye issue is very painful for the hammy. They scratch because of the pain as it is the only thing they can do.
I'd say she needs more than baytril by mouth but also needs a steroid / antibiotic eye drop to bring the swelling down. This is usually Maxitrol eye drops.
Putting the meds in the water is no use if it has been prescribed by syringe because they would need to drink the whole bottle to get the dose which will not happen. Persevere with the syringe and use the swaddling technique to get it in her. I'd say it should be working in 3 days and if not it needs rechecked. Dwarfs can get glaucoma when the eye keeps swelling and she will need the steroid drops to treat that.
An infection or abcess behind the eye is also possible and can come up from a tooth root. Has the vet checked her teeth? Again hard to treat and painful
If the abcess speads in to the brain it is very serious.
I really would consider having her rechecked if things are not better pretty soon.
Hope she rallies for you x