Hi, did you use neat tea tree?
Try putting it in a carrier oil like almond oil etc. If your cuticles are a bit raw then maybe the tea tree is too strong to apply it neat at the moment. You could also try putting warm water, not hot, into a bowl and adding a few drops of the tea tree to that and put your fingers in there for a few minutes. Alternatively, mix about 8 drops in a small tub of base cream that you can get from the pharmacy and just rub it on your cuticles.
Once the infection starts healing, you can start applying it neat again, but some people's skin is just too sensitive for that.
Hope this helps!
Good Luck