I would try to get a brace from your doctor that will keep your wrist in a more neutral position when working at your comp. Just do exercises that will not aggravate the pain. If it doesn't hurt then do the exercise. Also, use ice for about 10 minutes on and 10 minutes off. Make sure to do some stretching as well.

Where exactly is the pain BB?

on the bottom of the tricep, outside of the elbow

I looked up some information in my gross anatomy book and here is the exact details.

"Lateral epicondyltis(tennis elbow) is the most common painful condition in the elbow area. This elbow injury usually results from repetitive microtrauma of the common extensor origin of the forearm extensor muscles. Repeated forceful flexion and extension of the wrist strain the attachement of the common tendon producing inflammaton of the periosteum of the lateral epicondyle and the common extensor attachment of the muscles."

Therefor you want to keep your hand in a neutral position as not to extend the hand and aggravate the muscles. This is why a brace is necessary especially if you have to type all day. I would suggest seeing a physical therapist but many just wish to deal with it themselves. Good luck.