Short range fixes, like ibuprofen and only shooting a few arrows at a time, might get you through the hunting season, but tennis elbow is a long range problem requiring long range solutions. Tennis elbow usually occurs in the bow hand elbow, and is a result of micro tears in connective tissue that get inflamed. The micro tears can heal, but with continued irritation can become chronic, and at that point it takes longer to heal. The micro tears are a result of many tiny shocks, none of which are enough to cause a problem by themselves, but cumulatively they can get inflamed.
Once your immediate problem is solved, the best way to avoid recurrence is to minimize the shocks that cause the micro tears. The best way to do that is to shoot a bow without much hand shock, such as a heavier mass recurve rather than a light mass straight limbed longbow. If you can find a r/d heavier mass longbow that you like, that would probably work too.
Shooting fewer arrows and ibuprofen help with the pain, but do not cure the problem. Surprisingly, neither does total rest. To cure your immediate problem you need to avoid further aggravating the elbow with whatever is causing the micro tears until they can heal, and provide your elbow with the right kind of exercise that will promote blood flow to the injured area. I used Theraband Flexbars, available at Amazon and probably other places, and other exercises you can find on the internet involving cans of peas, etc. None of these exercises are hard to do; they are to promote blood flow to the affected area, not to build strength.