What kind of injury is it when the bottom of tricep to the elbow is hurting when I stretch my arm?

Likely tendinitis. The triceps muscles connects to the bony prominence of the elbow at the olecranon via the triceps tendon. Pain at the insertion site can be from the muscle, tendon, or bone. Overuse injuries commonly affect the tendon (tendinitis). Direct trauma or injury to the olecranon can also cause pain. The bony insertion site can develop a bruise, stress fracture, or actual fracture. X-rays can help here.
Tennis Elbow. Tennis elbow (or lateral epicondylitis) more than 100 years ago. Today nearly half of all tennis players will suffer from this disorder at some point. Interestingly though, tennis players actually account for less than 5 percent of all reported cases making the term for this condition something of a misnomer. There are 2 additional strain related conditions could be golfer’s elbow & bursistis.