I am about 50+ lbs overweight. I carry the weight in my arms, thighs, stomach, and butt. Am I going to have loose skin now?

Depends. On how much weight you lose, how much skin laxity you have to start with, your age, intrinsic elasticity of the skin, luck.
Saving Some Skin. The answer depends upon how much skin has become "incompetent" or has lost its elasticity in these areas. Skin is quite a resilient tissue and with massage and proper hydration can achieve much of its vigor. Sadly with age the collagen in the skin changes and so does this ability. The older you are the less likely it will "snap back". A plastic surgeon is the best resource for more assistance.