My skin broke out like that when I had undiagnosed Hashimoto's. I'm not saying you have a thyroid problem, but there's definitely something off kilter with your hormones. It's quite common for women in their late thirties and forties to have cystic acne breakouts. You need to tackle the hormonal imbalance, and there are various ways to do this.
For me, the following has worked (I'm 39, and have had breakouts off and on since I was 13).
Topical clindamycin/benzoyl peroxide. This worked a treat, but I didn't like using ongoing antibiotics, even if only topical.
Low-carb diet. Cutting out dairy. There was a study published in the BMJ saying that cow's milk products exacerbated acne issues in prone individuals, likely because of the hormones. So try cutting that out for six weeks and seeing what happens.
Yasmin. This pill was amazing, aside from the fact it made me blue. But my skin was flawless for the year I took it.
Saw Palmetto. Start with 160mg of the standardized extract, and add in a pm pill if you have no stomach problems (I didn't, and I have a sensitive stomach). This has been an absolute bloody lifesaver. I now have completely flawless skin, even right before my period. It blocks the effects of an enzyme that converts testosterone into DHT (responsible for 99.9 percent of acne in women in their thirties and forties). Spironolactone will do exactly the same thing, and that was to be my next port of call, but again, I'm glad that I found something that worked in a similar fashion but isn't a prescription medication.
Skin products. Meh. I've worked my way through everything from Clarins, to oil cleansing, to Proactiv, to tea tree oil, to...every outrageously priced organic line under the sun. I can pretty much use any product on my skin these days and won't break out, because I'm controlling the acne from the inside. I do drink three liters of water daily, and eat very little sugar, as again, doing this frequently elevates your insulin levels and disrupts other hormones. Being insulin resistant is very common in people with persistent acne.