Diagnosed with elbow tendonitis for two months. experiencing tricep spasms and odd finger tip sensation. is this more serious form or limited movement?

Possibly: There are multiple nerves that pass through the elbow to the hand and they can become involved in the process. For example, golfer elbow is an inflammatory condition of the tendons and ligaments on the inside of the elbow; the ulnar nerve also is near that area and when this gets involved one can get numbness running into the fourth and fifth fingers.