I had a tennis elbow on this June(2011) from climbing over hang walls. I tried same climbing problem again and again, and developed a sharp pain in my elbows.
I went to see a doctor and he said, "It's a typical tennis elbow. Just stay away from climbing or bodybuilding, and try to rest your arms as much as possible".
And yes, I did rest my arms for 2 months. It was boring but no other choice.
Is that all you can do when you have elbow pain???
Elbow pain is caused by over-use, or over-training of your elbow. So don't try to work out more, pain will get worse and worse.
Some folks may think making your elbow strong but that is totally wrong.
CUZ YOU'VE JUST OVERTRAINED ELBOW, SO IT HURTS!
Then, what can we do instead? Please look from different angle.
Scooby1961 has a lot of nice videos that show you how to make your arms bigger without harming your elbows.
If you want bigger arms, do triceps workout, not biceps. Triceps are bigger muscles than biceps. And biceps workouts like dumbbell curls is very isolated movement with small muscle group, so that it will put more tension on your elbow and, VOILA, tennis elbow!
So what can you do?
Triceps kickback. This exercise does not put stress on your elbow but trains your triceps well.
Skull Crusher with EZ bar works your triceps well and very shoulder elbow friendly. EZ bar does rid of extra tension from wrists and elbows. Please think of getting one.
Side raise may not give you enough pump if you are used to doing dumbbell fly or lateral raise. But holding your elbows tight does not put tension on elbows. Good exercise when you have elbow pain. This will give you bigger arms and shoulders!
There are other good tips from Scooby, so please check his Working Around Injury.
So although I rested my elbows for 2 months, I did my workouts with Scooby's advice. No muscle loss but more on arms and shoulders :-)
Dumbbell curl is a good workout but don't over do it. Don't be a curl monkey! Over training causes injury and muscle loss.
And, when you workout, try to train related muscle group evenly. Like train your biceps and triceps, or quad and hamstring. For the health of muscles, it is important to keep all the muscles in balance. Having huge quads and spindly little hamstrings is a recipe for knee problems. Same applies to other muscles.
Injury is very demoralizing, physically and mentally painful. So before working out, please learn and relearn the workout program, try to imitate good forms, and listen well to your teacher.
And even when you are injured, there's always a workaround.
If doctor tells you no workout at all, you can still read books and internet to workout your brain :-)
Actually brain is the BIGGEST muscle. Please train more!