A few years ago I developed pain in my right forearm and elbow, which I identified as being caused by repetitive use of the my right hand for computer mouse operations, in my then desk-bound day job operating a computer. Luckily it did not affect my playing too much, as the right arm does not need to support much weight when operating the slide. After trying various support bandages and braces, I found that the only thing that allowed the condition to clear up was to learn to use my left hand for the mouse and rest my right arm as much as possible.
About six months ago I started to get the same pain in my left forearm and elbow, coinciding with an increase in the amount of practice I was doing, especially high register stamina exercises where I need to provide some mouthpiece pressure against my lips, which puts quite a load on the elbow. This would come and go in severity, depending on how much playing, gardening or lifting I had used the arm for, until maybe about 6 weeks ago when I think I really aggravated it on a bike ride on holiday (didn't help that I jarred my left arm falling off trying to turn around in a tight spot!) followed by some rather strenuous gardening soon afterwards. Since then I have struggled with day to day activities, and playing un-aided has been quite difficult.
However I think it is now on the mend, as a result of being very careful not to use my left hand if I can, using a make-shift sling to take weight where possible, and by obtaining some support aids for my trombone which I will describe here. So here are some tips that helped me.
I started practicing 'left handed'. I found that by reversing my tenor trombones (not really practical for a Bb/F unfortunately) and playing as though left handed, I could continue long notes and lip flexibility/slurs practice. My right arm is now taking the weight and mouthpiece pressure forces, and my left hand only needs to keep the slide from moving. This might even be a useful skill in future!
I managed to find a second hand 'ergo-bone' trombone support on eBay. This is a support brace, that takes the weight of the trombone via a spring loaded rod attached to the slide where the left hand holds the instrument. The rod then either sits on your chair, or fits into a support on the front of a harness you wear. This makes holding the instrument much easier, fully supporting the weight of the instrument. For practicing it is very effective, however for performing it is actually rather cumbersome, especially if you have to change mutes. Douglas Yeo has written in more details about the practicalities of using this device on his page about reducing tension whilst playing, which I definitely recommend reading.
I also purchased a new Neotech Trombone Grip on eBay. This is a plastic and neoprene strap that is attached to the trombone and which your left hand fits into, meaning that you do not need to grip the trombone at all with your left hand. I think that it provides a similar sort of relief as the Rath trombone hand support albeit at a much cheaper price and less attractive appearance. I find that this relieves a lot of the tension in my left forearm, and I can actually use this in combination with the ergo-bone support.
I have found that these two devices mean that I can play without aggravating my arm and elbow, which quite effectively stops it from getting worse again. However, the thing that has the most effect with actually improving the condition for me are some exercises and stretches I found on this page. There are lots of other web pages with information about relieving tennis elbow, but the activities described here work best for me. I also found that a trombone mouthpiece is just about the right size and weight for me for providing the necessary resistance!
Before I finish I will just mention a few things I found that did not help so much, or are not recommended. I tried using a sports support bandage for a while. Whilst this might help a bit with elbow support in day to day activities, I actually found this quite uncomfortable to play with, as it tends to want to straighten your elbow and adds to the tension. I also have used a wrap around brace that applies pressure to the painful area. Again, whilst this does work to a degree (it was helpful with my right elbow) I find playing with it uncomfortable. I'm also a bit reluctant to use anything that simply masks the pain, as I feel I might be doing more damage unknowingly. I found some information that recommended applying an ice pack, and this does help with the pain. However further reading suggests that research might indicate that this can actually slow down healing of the tendon damage, so I decided to stop this. Conversely, applying heat (e.g. with a hot water bottle) does help me with the pain, and some information I found suggested that this might also be beneficial for the healing process too by increasing blood supply to the damaged area (note I am not a doctor!).
I hope that this info might be useful to other trombonists suffering left arm pain, so if you have comments or recommendations please let me know!