Go to a massage therapist or someone who does Active Release! If you have tendonitis you’ve got lots of little tears and scar tissue. Your doctor can give you splints, drugs, etc. but the only way to get the scar tissue broken down and realigned properly (real healing) is to have somebody work on the muscle itself. Painful, yes, but effective. Plus, they will work on the surrounding muscles which are probably also tightening up in overwork and compensation.
You should have this checked out by a doctor. I started with elbow pain about a year ago and was diagnosed with lateral epicondylitis (tennis elbow). Cortisone injections in January and again in May took the pain away for a few months each time, but they are not permanent solutions. This time I am attacking it with more conservative measures: seeing an Occupational Therapist a couple times a week (after another visit to the doc). The OT uses ultrasound, heat, massage, TENS unit. I have purchased a massager and am awaiting delivery of a handheld TENS. There are also strengthening exercises that can be done at home. The soreness is abating, I am happy to say. It takes time and disciplined therapy, but it does resolve (I am told!). I cannot crochet at all for now, and my knitting is down to about 1/2 hour a day. I wish you the best!
Welcome @knancyknits! This post is 9 yrs old so I think the problem is probably resolved one way or another by now. 
When I was much younger and learned to knit, I learned the English method. In other words, I carried the yarn in my right had and “threw” the yarn. I never had a problem. I took a long break from knitting while raising twin boys. Now that I am much older I am knitting. A couple of years ago I began to get terrible tendinitis in my right elbow. Never suspected knitting. Went to physical therapy and started using a band around my arm below the elbow. Not much relief. Some time ago I met a woman who was an extraordinary knitter. She was raised in Scandinavia and learned to knit as a toddler. She knit the Continental method wherein the yarn is on your left and your right had has much less movement , You pick up the stitches from the left needle. It turns out that this woman has become a friend. She is also a retired physical therapist. When I told her I was going to get rid of all my yarn and give up knitting she suggested that I try to chang the way I knit. She suggested Continental style would have less repetitive motion with my right hand. I was reluctant but gave it a try. At first I was a lot slower but my right arm began to heal. You can learn about Continental knitting on the internet. One sit I took a look at was www.craft sanity.com.
Good Luck.
I was just reading all the remarks about Knitter’s Elbow. I was diagnosed with bilateral ulnar nerve neuropathy in 2013 and had surgery on my right elbow in 2014 with an ulnar nerve release. About 8 months following that I developed “tennis elbow” and it wasn’t from playing tennis. Today, January 2018, I still continue to have pain in both elbows. It was about 6 weeks ago that I started knitting (by hand) again and found that my pain in both elbows and my tennis elbow has increased tremendously. ( mentioned “by hand” because I do have a knitting machine ). I am waiting for repeated EMG testing to be done to see the extent of the damage. I am going to try the Aircast that was mentioned and hopefully that will help. Thanks everyone for the advice.