The runny nose and eye are a vet problem not just the weight loss. That’s not just allergies. He needs to be tested for Pasturella which can be fatal. Any type of nose/eye discharge needs to be checked by a vet because it’s not simple allergies. Bunnies breathe through their nose, so any type of discharge can prevent that, which can kill the bunny.
About the weight there is no such thing as critical care hay, unless you’re referring to syringe feeding critical care? Don’t feed a lot of carrots or oats as that can lead to GI problems on top of any potential other issues. Stick to his normal diet and either add critical care as a supplement or you can even try some alfalfa hay. You said he won’t eat hay, but have you tried other types besides timothy? A lot of bunnies like orchard hay, so that’s one to try out. In general, if he’s sick, he’s going to lose weight. I think you really need to see a vet.