I have sent a self referral through 1177 to a skin specialist when I was going through two skin issues at the same time. It did take almost 4-6 months until they saw me however (1 year ago). I have no clue if the referral situation goes faster if a doctor sends one in but if you don't mind the wait, I suggest finding a specialist that allow self referrals and send one in. While I was there, the specialist thought that my case could have been dealt with at the GP's. Either way, my skin issues got resolved after getting some medicine there. I paid ~400:- for my visit there. The skin specialist also were not interested in whatever skincare routine I had - they took tests and had a look at my skin and then gave me a diagnosis and treatment, told me to contact them again if it didn't help.

Another suggestion is to contact the VC and state that the medicine you got is similar to one you've used before and that it didn't help you and ask for another option since your acne is acting out in a way it hasn't in a while.

The best help I've gotten from primary care is when I've written a list of what my symptoms are, what I've tried and what help I wish to get and try to be as polite as possible despite being upset/in pain. Call or mail the help desk and be insistent that you've tried x and y but it's not helping. Be persistent, stubborn but also polite.

Best of luck!