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Most surgeons will not operate for this condition until conservative treatments have failed for 6-12 months. Conservative treatments include rest, brace, oral anti-inflammatory medications, steroid injections and physical therapy.
You can have up to 3 injections into the elbow, and sometimes it takes more then 1 to get relief. As far as your physical therapy they should be doing other things then just stretches and strengthening like ultrasound, ice massage and using a TENS unit.
Hopefully you have been given prescription anti-inflammatory medications along with the pain medications. If not you should ask for a medrol dose pack which is a steroid taper pack and follow that by an non steroidal anti-inflammatory, I suggest Mobic.
You should have also been given a brace to wear.
Since you have already failed some conservative treatments surgery may be required for you. There are different approaches to this being actually opening the elbow through a large incision or arthroscopic which is less invasive. This will depend on how your surgeon is more comfortable. They will "clean" up the articular surface of the joint and repair in ligament/tendon/nerve damage they find. They will remove any damaged muscle they find and reattach good muscle to the bone. There are risks involved with surgery. Some of the risks are infection, failed surgery, nerve damage, loss of strength or flexibility and the need for more surgeries. You will have to have physical therapy after surgery and the time line will depend on how fast you respond, but on average this will probably be a couple times a week for up to 6-8 weeks. There are no guarantees that the aching and burning will completely go away.
My suggestion to you is to continue with the medications, get an anti-inflammatory if you are not already on one, do the exercises for you elbow you have been shown in PT, try the brace if not done so and try another injection. If you still do not get relief in about another 1-2 months then I would have the surgery.
Hope this has helped you. If you have any further questions regarding this please let me know. Good luck with your elbow. Have a good day.