Took avelox. Having pain across top of elbows when lifting with palm facing down. What's the name of this injury? How long can it take to heal?

Tendonitis. It is probably tendonitis. Avelox can cause tendon pain or injury. Usually it will go away in a few weeks. Rest the elbows, avoid the motion that hurts. Ice the elbows for 15 minutes twice a day. If it does not get better see an orthopedist or rheumatologist.