This will probably sound a bit strange but I find tendonitis gets much worse if you support your head with your hands when you sleep.

If you are a side sleeper and habitually put your hands or just one hand (particularly the hand on the same side you are sleeping on) under your head or pillow you can be putting a great strain on the tendons, nerves and ligaments in your hands & elbows.

For someone who doesn't do any climbing or pullups it's of no consequence but if you are in heavy training or even just doing a lot of climbing, the tension though your hands and elbows is multiplied times 10+ if you sleep like that. So when you are asleep and should be recovering from the days training you could be stressing the crap out of your hands and elbows & aggravating the problem.

If I sleep on my side when I've been training pullups I get tendonitis every time if I sleep with my hand tucked under my pillow or my chin. So I basically had to train myself into different sleep habits.

I'm not saying this will be what's causing your issues but it could be something to look into, if you wake up on your side and find one hand tucked under your head or pillow give it a moments contemplation and evaluate the amount of tension in your hand and elbow on that side. If your hand is numb or your elbow is sore it could be a clue.

All I had to do to solve my problem was swap the hand that I tuck under my head to the top hand. If you use the hand that is on the side you are laying on chances are you're stressing the crap out of all your tendons, nerves and ligaments on that side.