As you get older most folks are going to have “pain”; however, most don’t think about it until they are forced to. Playing aggressive sports when young, being Special Warfare in the military… past surgeries… well, you just accept pain. Then, hopefully, the smart light turns on from within and you start to think (most folks call it “maturity”). Such is the case with your elbow pain. Pain is a guiding light.
Most of what Rob stated above I can go along with; however, I would suggest MICE instead of RICE. It will allow for faster healing time.
"M" for slow range of movement... as much as you can up to the point of discomfort, but NOT into it, or thru it. Your goal will be to increase range of motion SLOWLY… don’t look for leaps and bounds. If there is swelling, the slow easy movements actually pump the congested material out of the area. Of course, rest is necessary, but… just laying there? My thoughts? Move it or lose it! Work smarter, not harder… get results that can last.
Also, for some folks... Heat works better than ice. Saying that, try what works for you, and your body. If it’s Ice, ice cubes work the best, not the cold packs. (Vasodilatation will occur automatically at approx. the 15-20 minute mark.)
Just for reference: At one point, Tennis elbow and Golfer's Elbow were both viewed (along with many other injuries) as “Tendonitis”; however, studies have proven most of these concerns are actually overuse injuries (tendonosis)... not inflammation (tendonitis).
So, many folks are still be diagnosed with "tendonitis" yet a major portion don’t have “…itis”. I can’t remember the percentages, but I think it’s less than 10% of the diagnosed repetitive stress injuries are actually “tendonitis”. So, why do doctors still use the word “tendonitis”? I would think it's just easier for the patient to accept the tendonitis word (that way the doctor doesn’t have to explain the difference).
Still, I would suggest you get a referral to an Orthopedic / Sport Physician to rule out "other things" first. Then find a PT (with manual focus) or knowledgeable – full time - Massage Therapist (one with an orthopedic focus...not spa back rubbing treatments).
Some folks go to an ND because they’ve tried doctors / medicine with no results, and it just so happens that the ND’s solution worked. To me, it doesn’t matter… doctor, naturopath, or the dog Vet… if it solution worked… it worked! After all, go to Wal-Mart and you’ll see rows and rows of topical angelicas (Ben-Gay, Icy Hot, Tiger Balm, ect.). What works for one will or may not work for someone else.
I've been providing orthopedic services for the past 16 years... this is just my two cents.