For the Alliance, you can buy most things from a Vendor named Deneb Walker in Stromgarde Keep (Arathi Highlands). He sells the Expert First Aid Book (150) and the Heavy Silk Bandage and Mageweave Bandage Manual. The only one that I have not been able to find is Strong Anti-Venom Manual which seems to be drop only.
To get passed 225 First Aid, you must visit the Physician in Theramore (Dustwallow Marsh) and take his test by healing the injured patients with the bandages he gives you. Make sure you keep track of which ones spawned first, and take care of the CRITICAL patients first followed by the BADLY injured ones and lastly the plain injured ones.
Once you pass his test and are high enough in First Aid, you return to him and he will train you in the Heavy Mageweave, Runecloth, and Heavy Runecloth Bandages. I was able to get myself up to 300 with just Heavy Mageweave, but hope this helps you out.