I had a double mastectomy a week ago. I have swelling under my arms. Should I use an ice pack to relieve the swelling?

In general I advise my post-mastectomy patients not to use an ice pack, and there are several reasons for this. The cold may compromise blood flow to an already compromised area, thus leading to delayed wound healing. Another possibility is that you can get frostbite, as the nerves in your under-arm area may have been affected by the surgery and unable to warn you when your skin is getting too cold. Of course every surgeon has his/her own preference, so I would defer to your reconstructive surgeon to definitively answer this. There is no right or wrong answer. 

What you really need to do is see your surgeon ASAP to be re evaluated for this swelling in axillary area.