It is great you are having such mild pain, the ice machine probably helps with that, wish I had thought to get one to help with my recovery.
I was aloud to remove dressings and shower 2 days after surgery. Make sure you use waterproof bandages on you incisions and when you shower hold your elbow close to your body. I have noticed in several post that some people have used a cloth sling so they wouldn't "forget" and try to reach for something. You might want to call your doc to see what he says, they all seem to be different.
Getting yourself dressed the first time will be an experience

I found that button ups are best the first few weeks, just make sure you put the "bad" arm in first and when you take shirt off "bad" arm comes out last.
Hope you have a speedy recovery.