375 is the hard cap for all professions, and First Aid is no exception. Occasionally you'll see people talking about having 380 Jewelcrafting or other tradeskills just above 375, but those little boosts come from racials (+5 JC as a Draenei) and other augments (can get enchants to gloves that increase mining/herbalism skill).
When WotLK goes live and the hard cap for first aid is raised to 450, you'll probably have to push to 405/410 skill on Heavy Netherweave bandages before you can train the next category of bandages. (ie. currently, you have to make Heavy Runecloth bandages to skill to 330 first aid, then Heavy Netherweave at 360).