It's called "golfers elbow"gripping the paddle to hard,the missus reckons its from its from gripping something else 
Sorry. Couldn't resist.
Sounds like tendonitis. Inside of the elbow is related to biceps and lats. If your a weights guy, you need to ease off those muscles for a while and stretch them as many times a day as you can manage. Stretch your forearms too. Use some magnesium and anti inflams will help also.
Yes had that problem for years and still do to some extent! Guessing it is tendenosis which is different to tendinitis. Get your self a squeeze ball and light weights to do bicep curls and use them daily without straining the muscle, if it hurts to start with build up slowly and increase when it hurts less.
Worked for me and only flairs up from time to time but it can be managed, Google tendenosis it explains the difference and how to help it.
Quit playing tennis, you didn't say that you did, but this is one of the major causes of "paddler's elbow". Or get a girlfriend if you are not married, but if you have one, tell her to step up her game. We can only take care of so much by ourselves.
sounds like golfer's elbow. when that arm is your bottom arm you're likely gripping and pulling super hard with last 3 fingers perhaps.
loosen the forearm muscles on the palm side of your forearm by rolling your arm over a tennis ball back and forward as a start - but have a really good 'feel it out session' when you paddle next and feel what your bottom hand is doing in your stroke, try a pinch grip (just thumb and first two fingers holding the paddle) for a few strokes - if you're using your top arm well, you should be able to still grip the paddle with your bottom hand two fingers and thumb. Do a few strokes like this then add your whole hand grip back in and think relaxed
