I am feeling pain in my elbow - is it tendonitis and how can I fix it?

Overuse vs injury. Tendinitis is likely if you have an overuse or cumulative trauma type injury. Localized pain directly over the tendinous origins of your forearm muscles that worsens with resisted activity is a hallmark of tendinitis. The outer prominence (lateral epicondyle) is a common site for tendinitis and is painful with resisted wrist extension. Stepwise treatments: rest, ice, nsaids, brace, and injection.
Tendinitis likely. The most common causes of elbow pain involve tendon inflammation or microtearing of the tendons on the outside of the elbow (lateral epicondylitis) or the inside of the elbow (medial epicondylitis). Treatment involves rest, a wrist splint, icing and nsaids for acute cases. Injection therapy is often effective. Steroid injection for acute cases, platelet-rich plasma for chronic cases.
Maybe. Pain in the elbow can be many things including overuse tendinitis, osteoarthritis, loose body, cartilage injury, synovitis. Best to see your pcp or specialist and give a detailed history with xrays to rule of any bony causes. If it is tendinitis this can be treated with different modalities including physical therapy, immobilization, or injection. In refractory cases, surgery may be an option.
If a cause is known. A person who gets a numbness, soreness, or tenderness (to pressing on it) where the muscles attach near the elbow may have tendonitis . . . But he will usually know what caused it. The cause is overuse of the arm during the past day or two. Icing the sore spot and taking some Motrin can help. He can wrap the sore area with an over-the-counter elastic band, which will spread the muscle's force out.
Could be. Thing to be aware of is that very often the key is not in resting the elbow but in resting the forearm and wrist, because the muscles that connect at the elbow and that are affected by the tendonitis control the wrist and need to heal.