I have lots of experience with Golfers elbow which is the inside bony point of the elbow but it hurts just as much as Tennis elbow and is equally as disabling. I spose I should be grateful its usually only 1 arm at a time that is bad.
Anyways , for almost instant relief I use ice-packs. If its really really painful say YES when offered a cortisone shot. They sound scary and seem bad but give long-lasting relief even from chronic conditions.
Depending on whether or not the nerve is damaged or just being intermittantly squished it could take around 3 months of rest for the nerve to recover...I know its a long time for an arm to be out-of-action,. so maybe investigate some steroid shots to speed the healing process. Splinting of the arm in a neutral position at night can also help. Try these options before you consider surgery.
P.S....Google has tons if sites with info on Tennis elbows (Lateral Epicondylitis).