Hi OP,
I had awful awful cystic acne as a teenager and the many doctors I saw were pretty adamant i'd grow out of it and refused to really do much more than some short courses of lymecycline and offer me patronising platitudes. Nothing over the counter worked, it's just not strong enough. The antibiotics weren't strong enough - a lot of the advice being offered above is suitable for spots but not acne, which is written into your DNA and no amount of clean flannels and Benzoyl perozide cream will really go any way to helping.
Acne is not a hormonal condition as someone said above - it is a bacterial skin infection. It can last into adulthood depending on the type of acne it is.
I gave up in the end and just endured, but when it was still active in my twenties, I paid to go to a private doctor to ask them about laser treatment for the severe scarring. They wouldn't do it without me undergoing proper treatment to ensure the acne was no longer active, so wrote me a letter suggesting a course of roaccutane/isotretinoin which I was to take to my NHS GP. It worked and I was on the waiting list for roaccutane within a week. It was a six month wait, and a very tough treatment to go through, but very successful. I now have the kind of skin I dreamt of for years.
It is easier for boys to be referred for it than girls (speaking from personal exp.) as the risks of the medication include serious birth defects if you were to become pregnant whilst taking it (obvs not a risk for your DS - but something that will be in his favour).
The dermatologists I saw at the hospital couldn't believe that GPs during my adolescence hadn't taken me seriously (my scarring is very severe across my neck, back and chest) and told me always to just kick up a fuss, ask to see different doctors, complain if it wasn't being taken seriously.
Acne leaves physical and psychological scars that last forever, it's a serious medical condition. My heart goes out to your DS - there is treatment out there. The private doctor's appointment cost me £50 and was the best money I have ever, ever spent. If you are able to afford that, then it might be a good route to go - the actual roaccutane treatment is on the NHS, it's just getting that initial referral that you need.
Best of luck OP - fight for the right treatment for your son, I promise it is out there. It's just not on the shelf at Boots!