Not sure on the pop. As suggested, it might be worth your while to get it looked at if the severe weakness lingers. In addition to tearing a tendon, you can actually pull off a piece of the bone where the tendon attaches to the arm (avulsion fracture). If it's a simple tendonitis, that's an easier can of worms. As a PT I can give you a biased recommendation to see a PT if this lingers as well. My specialization is in other areas, but I've treated a good bit of tendonitis through the years. As for yourself, you can do ice massage to the most painful areas for 4-8 minutes until it goes numb several times a day for a week or so, and you could also probably learn to do a cross friction massage to the tendon as well. After things start feeling less tender, you can start doing some gentle stretching. One of the best ways to help it heal and avoid it coming back is to strengthen the muscle eccentrically. Again, a PT could give you some specific exercises in addition to other modalities to help it along.
Joe's tip of using a brace is right on as well. They're typically called tennis elbow straps or epicondylitis straps. The reason you start having trouble, whether it is on the outside or inside of the elbow, is that a number of muscles have their origins right on or around the little bony point on either side of the elbow. That small area takes a lot of force and stress and can become irritated with repetitive over-use or trauma. The straps/braces help support the muscle, providing a more broad area of pull and taking some of the stress off of the epicondyle.
--nathan