I wouldn't syringe him. At this point that would just cause more stress then it would be worth it. When they panic, they can fight quite hard! Treatments like this should be last resort..
Just use a smaller water dish, so you can frequently refresh it, you can also make sure he actually drinks it by keeping and eye on the water level. If he doesn't seem to drink it, I would also offer regular water. You want to make sure he keeps drinking, even if its just plain water.
I think he will be fine, you are very caring and on top of what should be done. Correct husbandry and a good long rest from eating and handling is the main thing for now. After that, take it slow and easy for a bit.
Listen to Kara, I believe she is the most knowledgeable person when it comes to Bloods and I would trust her implicitly with any advice she has regarding their care and recovery.