I'm 54, right handed, and got tennis elbow in my right elbow. Likely got it from hitting lots of balls on very hard turf late in the summer here in Chicago. There was still a few months of golf left in my season so I did not want to take time off. I ended up taking one week off. I can not take anti-inflammatory drugs for other health reasons.
Started PT multi times a week. Electric stimulation, ice, heat, stretches, exercise -- all based on PT's plan. I played golf through it all. I reducing range work (fewer balls, more teed balls).
Wore an tennis elbow strap when doing anything that used elbow including golf and mowing the lawn. PT recommended strap over a compression sleeve. That strap allowed me to play without pain or fear of making it worse.
Wore a thumb stabilizer to bed (very sexy). Seemed like an odd thing but PT said sleeping positions can slow recovery and a stable hand helps.
Got new "graphite" shafts in irons -- Aerotech composite. Great at lessening impact and great anyway.
Did recommended exercises on my own. Got a Therma-Band Flexbar (red) and it really helps. Could not even use it without pain at first and now it doesn't hurt at all.
Several months later, elbow is almost like new. I'll wear the strap while golfing this Spring because it does no harm to my game and it allows me to feel confident that I'm not going to re-injure the elbow.
My advise based on my experience -- take it seriously, find a PT you trust, and do what the experts say to get better. Don't try this on your own.
Good luck on your road to recovery.
for your information: