It doesnt matter if its called tennis elbow, golf elbow or masturbation elbow, the end result is that where there is pain in a joint its likely do to injured tenons or ligaments.
The cells in the tissue that makes up tendons/liniments has a very slow cellular turnover rate (ie 300 to 500 days normally). Swelling is a key element in the healing cascade and why in many areas it can be very problematic, in the case of tendons/ligaments eliminating the swelling and reducing blood flow with ice SLOWS healing and masks pain. You hit the gym, do more damage, take more NSAIDs/ICE, rinse repeat until you finally suffer permanent damage or a separation. When one gets injured it also puts additional stress on the rest of the joint making surrounding tissues more likely to be damaged as well.
Allowing it to heal is the only way to truly make things better, you can speed healing with prolotherapy but aside from that lifting the way ya have been and masking the pain and reducing inflamation is just setting yourself up to fail.
Just to add, some time back I had tennis elbow so bad I couldnt push a door open at the mall without having throbbing pain for hours afterowrds. Tried all the typical "regular doctor" BS of ice, NSAIDs etc and when that and a few weeks off didnt do a damn thing I returned only to be told a cortisone inj was they key. I wasnt worried about the injection, but the long term effects. After doing a lot more research I came to find out cortisone injection was the WORST thing I could have done if longevity mattered.
In the end I turned to prolotherapy, had both elbows treated and never even had to stop lifting. I missed a day here and there after each treatment but didnt give it up all together and within a few months was back to normal. It worked so well on my elbows I had a foot treated, a shoulder I separated earlier that was giving me problems and my back as well. Even recently I went back and had a finger treated that I sprained real bad and just keep catching it on stuff and aggravating it enough so it never seemed to heal.