If you had no problems until recently then are you sure it's from the previous injury and not another injury?
You can do what you like, but the body does not respond well to training injured.
I'd rather see 2-3 different doctors and get different opinions, maybe use some cool equipment like an MRI,etc and make sure nothing is torn instead of try and rehab it yourself.
If it's not torn then go for it. But if you have even a minor tear, every time you try and perform an exercise that involves the triceps, whether directly or indirectly you will aggravate it and it will NOT heal.