First, I like to say the strap that you brought will only help temporary. In the long term...it will make your muscle weaker. What you are having is muscle imbalance. You are ultizing too much of your gripping motion (forearm muscles). To off-set it...you have to do this particular stretch.

In this picture.....I am placing my left hand open and flat onto the wall (Use your arm that is hurting) Make sure your elbow is straight. Then you take your right hand and grab your thumb underneath your arm. I took a picture with my right hand hold camera and not able to hold my thumb. :) Make sure you grab your thumb away from the wall while your other fingers is still flat onto the wall. This will help to balance your muscles. If you can...avoid gripping your hands as much during the days. Also, buy fresh ginger roots (slice it) and boil it with water to drink it. It is an anti-inflammation will help to reduce the swelling and pain. If you like...buy fresh pineapple and eat it. Its great to reduce inflammation as well. Good Luck!