With all due respect to all, rest is NOT the thing to do. Yes, you do need to have periods of recovery and in severe cases of injury, rest (i.e. not exercising the joint/muscle(s)) may be the only option for a short or intermediate period of time, such as with a broken bone...but even then, there are modalities which will not only help you to recover more quickly, but also to a point where you are actually stronger in the region of the injury, barring such nasty usually age-related realities like auto-immune diseases such as arthritis.
That said, you need to know what you are doing and really focus on the exercises as you perform them. Additionally, it will help immensely if you get in good cardio shape and get lottttts of sleep. You will need to perform specialized exercises which target the injury and do lots of very clean reps with relatively light weight...which will increase over time. You also need to do what I call bulk exercises which are the common exercises you would do if you were healthy...just less of them at first and with lighter weights than before and after. Done wisely, this will help the injury heal and prepare you for a full work-out when you heal up (actually before you fully heal). Oh and very important: STRETCH and STRETCH. You may need someone to show you how to do special stretches...someone other than the recent high school grad/junior college student 24 Hour Fitness pays $10 an hour to pretend they know something.
Meals are important...Plenty of timely carbs and enough (no shakes necessary) protein. Fat is to be minimized.
All this said, you will run into no shortage of "experts" who will tell you that you need to sit on your a** or even get surgery, etc. 99% of the time, this is nonsense in the case of chronic nonspecific-event injuries. Yes, if you tear a miniscus or something along those severe lines and are highly athletic, surgery may be necessary. But usually no. And be careful with NSAIDS. Doctors tend to recommend them or prescribe them like they give out candy on Halloween. Stay away from them as much as possible. Ice is good, but this too is an art. Done improperly, at best nothing good will come of it...At worst, minor damage can be done (rare though). Done right, it can be one of your best friends. Ice is fantastic, done right. I'll explain later if you wish.
One last thing, in the case of the elbow, the common belief is that full range is to be avoided. Hell, that seems to be the consensus for all exercises these days. Short of calling BS on that (which I personally do), you need to make that decision yourself. If you do decide to go full range, know what you are doing. You will have to reduce the weight a little bit and may need a spotter at first. That aside, you should know that with elbow rehab, full range exercises done with an almost exaggerated light weight will help you heal like nothing else. Done with correct stretching, you will be amazed at how much better your elbow will feel. It will be like the fountain of youth! Your elbow will feel better than it has in many years...and it will be permanent.
All of this is stuff you need to be shown, rather than told. Once you get in tune with your body, provided you are relatively intelligent (which I'm sure you are) you will be able to figure out what works and doesn't...over time, with experience. Be patient though.
Good luck.