I would watch for oil-free products that say they are for "sensitive skin", and then test on a small area first rather than all over. If it breaks you out or otherwise doesn't work for you, many businesses will take it back, so save your receipts.
I had exquisitely terrible acne the whole time I was pregnant and nursing my first two kids (so for about two years a pop). My face would rip open at night and bleed on my pillow (it was that bad). A week after weaning the second one (when he turned 12 months), I started clearing up, so for me it is totally hormonal. With the first one, a friend at work gave me some Benzaclin (a prescription that she didn't end up using, but offered it to me because of my obvious problem). It has benzoyl peroxide and the antibiotic clindamycin. It cleared me up in two weeks, and then I went to a doctor who apparently didn't know anything about what is ok when you're nursing, and she refilled the prescription for me as needed. But the OB wouldn't give me that when I was preg/nursing the second one, but there were no ill effects on my first son, that we know of.
I went through accutane after weaning the second one, and so (as happens) my skin became extremely dry. I mistakenly put a vaseline product on my face one night, and didn't even break out (that's how much it dries you out). The dermatologists office recommended several products, including Eucerin Calming Cream (I think that is what it is called). They also said that there is a difference between "lotion" and "creams", where lotion often has alcohol and such in it, but cream doesn't. I don't recommend doing accutane, by the way. It is too risky, and only "cured" me while I was on it. I still break out, according to my hormones. Best wishes to you, and believe me I understand your frustrations.