Definitely get it checked out and look at the ergonomics of your work setup like the previous posters have said. The longer it's left, the longer it will take to heal.

You can use ice massage on your elbows to help the inflammation and pain. Get some polystyrene cups and 3/4 fill them with water and freeze. Take one out of the freezer and remove some of the polystyrene so the ice is exposed, and rub on your skin in circular movements for a minute or two until it feels cold, cold, cold. You can do that 2-3 times a day and I swear it helps. I do it on my elbows and wrists after cycling, and sometimes have it done on my lower back if I have back pain. The back ice massage is akin to torture and half the neighbourhood hears me scream, but the elbows and wrists are much easier to do