I’m so sorry OP that you suffer this. Acne is horrendous I know.
I have swarthy olive oily skin and throughout my teens my spots were awful, just horrendous and in my early 20’s during the 90’s, I developed acne. It totally ruined my confidence having such bad skin at uni really at a time when I should have been dating more, having fun and in the prime of my youth. I became quite reclusive and it greatly affected my mental health - I just barely manage coping with it; endless skin care, make up etc. Every day cleansing, popping, tcp, toning, make up trying to hide the cysts - omg it was awful.
I tried everything in those days from Clearasil, Clinique to herbal remedies- nada. I knew it was most likely my sebum oily skin and hormones.
My parents then paid for for me to see a private dermatologist and I was put on tetracycline for 2 years in about 1992-3. Took a while to get going, but it worked an absolute treat! Once my skin had really cleared it stayed that way for good. Although I still got lots of spots, my deep acne left me forever and it was manageable from then on. I still have a few scars around my chin and jaw line but nothing that shows much and a little make up covers it.
My children are all now spotty teens and have my skin tone. So if it gets worse any any develop even a hint of acne, I won’t hesitate to get them seen privately and on antibiotics or similar for however long it takes. I know rouactane has some bad side effects, so obviously I would monitor that with them but for me, the tetracycline was my own massive turning point.
Now they have accutane ( in the 90’s there wasn’t much available then apart from tetracycline) like others have said, please try this. I won’t let my children suffer what I went through so it’s worth pursuing every angle for treatment.
I’m not sure how much use the NHS would be. Definitely see another GP and ask for a second opinion- you’re entitled to that. I find the NHS sometimes unhelpful. They won’t prescribe any pills unless you’re literally dying now; they seriously gatekeep ; you get fobbed off or told to take paracetamol for a month and go away. Sorry to say that but that’s been my experience.
My acne was both hormonal and due to my oily olive skin which produces a lot of sebum. I’m in my late 40’s now and use only a mild anti ageing moisturiser and I STILL get a few spots around my period and maybe some peri menopausal changes. Almost 50 and I’m still popping spots!
I find retinol breaks me out in spots and if you use it, you must put an SPF on your skin the following morning adding to what you’re putting in your skin already. So be careful with retinol. Get proper advice.
I think it heavily depends on your skin type and age . You need a professional consultation/ dermatologist to discuss your options. Try a good complimentary herbalist as well. Some have great advice as to how to work naturally with your skin type. I find eating almonds and nuts and avocados by the shed load keeps my skin smooth but then I’m middle aged 
and have different skin needs.
Seriously, don’t let a doctor ignore the issue. Insist you need a referral and you’ve tried everything from diet to skin routine changes, the pill etc - nothing has worked and it’s affecting your mental health / confidence. Acne is very painful too - no doctor should ignore it but I have found some doctors unhelpful about all sorts of issues so insist you are helped.
But it’s really worth the money if you can save up for it to see a specialist. You’ll be seen quickly and helped. Good luck and definitely look the antibiotic/ accutane route.
I found no over the counter products helpef me ( although I’m going back 20 years!) But Weleda are one my favourite skin care brands- I love their natural cleansers and products; they are natural and very gentle.
Both my girls use their new product called ‘Acknedoron’ for problem skin - it works well for both of them. It just take the edge off spots and is very calming as is their Almond range of cleansers. My older daughter uses La Roche Posey Effaclar too which she says reduces redness with her spotty skin and it’s reviews are excellent overall plus not too expensive.
Sallycallic acid I’m sceptical of - if you strip all the oils out- your skin tries to make more ! But again, it depends on skin type.
I really hope you manage to get treatment -don’t leave it any longer OP.
I used to keep at hand some heavy duty theatrical style foundation that covers scars, acne, burns etc for if I needed to cover large spots etc. I don’t recommend you use it all the time of course but for special nights out or important functions, there are some really excellent foundations on the market that can cover acne well so you feel more confident and less self conscious. Very best of luck and like a lot of ladies on here - my advice is the same; antibiotics/ accutane. 