I naturally have 'hormonal' oily skin and, as a pre-teen I had terrible acne and big crops of blackheads. I used to use harsh stuff designed to dry them out, like clearasil and clean & clear. It took me ages to work out I was actually making them far worse!
What worked for me was a very gentle foamy type cleanser used with a flannel (gentle scrubby action) in the morning, after school and night, a very light moisturiser (otherwise the skin compensates by pumping out loads of oil), I did GENTLY extract blackheads and squeeze spots but with clean hands, tissues and minimal pressure, applied either neat tea tree oil or Clinique's blemish gel on really bad spots and a couple of times a week I used a deep cleansing clay mask.
Try gentle skincare ranges, without too many nasties in them though, like Neal's Yard. If price is an issue, Neal's Yard often comes up cheap on EBay, due to the party plan reps either giving up and selling off stock or promotions.
Rather than doing a major weekly exfoliation with a grainy type scrub, it's better to exfoliate every time you wash your face, using a flannel/muslin type cloth, ie: taking off a thin layer every time, rather than potentially aggravating the skin by 'blasting' it. BUT: the cloths must be kept clean and changed on a daily basis, due to bacteria.
Now I'm nearly 42 I LOVE my oily skin as it isn't wrinkly! But I can still get a bad breakout along my jawline unless I keep it scrupulously clean and well exfoliated - I use a Clarisonic nowadays, which is amazing! They are pricey, but really work wonders in my experience. If I'm lazy and forget to use it, I get spotty again. You can effectively try one for free if you buy it from QVC under their 30 day guarantee - they have cheap pricing / offers too. Most Clarisonic kits come with an acne brush, but I just use a normal one.
By the way: my twin nephews (13) were quite spotty, so I bought them a kit each for Christmas (as above) and it appears to be working.