Eek! I'm not a PT, but maybe you should consult with one. That just does not sound right.
There are many, many ways to work your tri's, tho. Do you have access to a stand-up pulley machine? There should be a diagram on the machine that maps out how to work tri's right on there.
If not, you can work your tri's by doing other exercises besides laying down. Do you want me to list them? IDK if you've tried any of them and have had the same prob...
But I guess my point is, every BODY is different. If your limitation is not due to injury and just due to how you are built, try all the different methods of tricep exercises to find your niche.