bro, I could write a book on this subject. I am at the tale end of dealing with the injury you speak of on my left elbow and forearm. last year at this time it was my right elbow and forearm.
first off, anti inflammatories are a necessity. I am a Highland games strength athlete, and I train heavy year round. ice may seem like it's not helping but it will over the long haul. depending how bad you have this, it's known as tennis elbow on the outside bone of the elbow, and golf elbow on the inside part.
there are straps you wear around your forearm that are about an inch wide that will work if you keep them on. if you caught the flare up early enough. elbow straps allowed me to train through the injury.
my doctor gave me Celebrex and it did help immensely, but I had to avoid certain exercises such as upright rows, cleans, that type of motion. believe me, I've had the issue several times, to the point where I couldn't grip and lift a glass of water.
I am 45 years old and have been training for almost thirty years now, so I've been through this frequently.
As much as I dislike cortisone shots for shoulder injuries, it is an anti inflammatory and one shot pretty much cleared up my elbow and forearm this time, allowing me to stop the Celebrex.
I'm not sure about you, but resting the arm did not help at all, it seemed to worsen it. light movement to get blood in the area was far more effective.
Having blabbered on now, I would encourage you to try that forearm strap from your local pharmacy, depending on arm size you may need the knee strap, as I did.
one more thing, if you use heavy dumbells on say incline presses, don't let them snap back down to your thighs at the end of your set, drop the fckers. that's what flared my elbow and forearm up this time.
hope this helps you and anyone else who needs it. good luck.