M.R.
All of your issues also happened to me shortly after the birth of my daughter. It started getting better after I stopped nursing but still I have breakouts and my hair falls out, although not as bad as before. (my daughter is now 22 months.) I haven't found anything that truly helps other than washing my face every night before bed, keeping my hair off my face and constantly changing my pillow case. I think both are just linked to the new change in hormones.
Sorry I don't have a better answer but wanted you to know that you aren't alone and I think it happens to all mommy's :) Oh the joys :)