Good for you!!! It's so gratifying when you get to a point where you are playing *music*!!
I've been playing off and on for 30 years, and I STILL enjoy picking up a guitar an playing through some nice slow 12 bar blues!!
Definitely let your fingers heal. You don't want to injure youself. You'll find that after your fingers heal, you'll have some nice callouses on your fingertips. As long as you play consistently, those callouses should remain and you won't have to go through the pain again. It's like going to the gym - it's painful getting in shape, but that goes away and stays away as long as you remain in shape. Skip the gym for a while, and it becomes painful again :-).