It will depend on your age and family tendency to have acne, but certainly PCOS could also be playing a part. If your testosterone levels are elevated due to this condition, you could be secreting an excessive amount of sebum, which may be difficult to control.
Unfortunately, if the condition is severe, it can be very difficult to control the resulting acne and it is certainly worth discussing with your GP or Gynaecologist.
What you can do may be enough to control the worst of it and you have clearly tried a few topical treatments.Some people have great success with the three you mentioned, but they may be a little harsh for your skin and result in more inflammation rather than less.
The first thing is to ensure skin is kept clean and you are taking enough water and vitamins A, C and E in your diet. Various B vitamins can also help and if you get a blood test, it might be a good idea to check that you are not deficient in any useful trace elements - especially zinc and selenium, which need to be available for skin to function well (too much zinc can be dangerous, so, if you are taking supplements, don’t take more than the daily recommended amount.)
I would suggest that a gentler approach might allow the skin to repair itself better. If you use a hydrosol to clean your face, remove makeup and ‘tone’, you will get the benefits of the botanical constituents and not upset the skin’s pH. Calendula is an excellent skin-calmer, it has anti-inflammatory, anti-viral and anti-fungal properties and soothes acne and redness in the skin. Honeysuckle is a powerful antioxidant and anti-inflammatory, with a high luteolin content which is very soothing and helps the skin strengthen. Like Honeysuckle, green tea contains excellent polyphenols, including EGCG (epigallocatechin) which track down free radicals and can strengthen skin. Algae can also help, Bladder wrack is good for acne. Evening Primrose is an astringent that will counter oiliness (you must avoid this one if you have epilepsy). St John’s Wort is similarly astringent due to a high percentage of tannins. It is also anti-inflammatory, anti-microbial, anti-fungal and anti-oxidant. (It contains hypericins, so must be avoided by anyone with a known allergy and it shouldn’t be used if going into the sun as it can be a photo-sensitiser too). Aloe vera is always worth a try, it works very well for some people and not at all for others, but you may get lucky - do buy this from a reputable seller or you could just be applying glycerine (or worse) to your skin. If you can, grow one in a pot and use it fresh.
I would still suggest you use a light moisturiser (often people with oily skin avoid anything containing oil, but these can be helpful, rather than adding to the problem - what skin actually produces is sebum which is more accurately a wax, rather than an oil) Look for allantoin in the moisturiser, this is a keratolytic, like Salicylic acid, but gentler, so it will keep the pores clear and free from debris with a slight anti-inflammatory effect (.5–2% in a product should help). Colloidal oats are very soothing and often over-looked, these can really help, either in a face-pack or in a cream. If you want to use an AHAs, I would suggest considering a PHA instead, like Glucono delta lactone, it is gentler and effective at .5%.
If you are over 30, finding a produce with Glutamine at about 5% can help the longer term restoration of the skin. Again, looking to build up the skin, if gradually, I use peptides and ceramides in most of my moisturisers - often with vitamin C and ferulic acid to really boost the skin’s ability to heal. You need to be careful when selecting peptides, there are thousands and only a few are useful. They need to attach to a lipid molecule, fit the right cell receptor and are susceptible to damage caused by the wrong pH and heat….however, the right ones can make quite a difference (getting these in your diet is also a good idea). Look for urea and witch hazel too as all these can improve the condition.
There are essential oils that are used, but I suggest that you work on calming the skin before ‘treating’ it as such. Rose, geranium, vetiver, helichrysum, lemon and frankincense have all shown to help some people with a similar problem. But essential oils are especially dose-dependent in terms of healing, too little and they do nothing, too much and you can cause dermatitis or worse. So do buy from a reputable seller and use a good EO guide to instruct dose - I always use Robert Tisserand’s Safety In Essential Oils, if I am in any doubt.
I would concentrate on calming the skin and reducing the inflammation first, then, when it is feeling comfortable again, add the above mentioned ‘extras’. It is difficult to say which will help as we are idiosyncratic creatures, some people find relief from two days of aloe vera and other need a combination of half a dozen ingredients to see an improvement. So I would try to keep it simple, if something isn’t working, stop using it, bearing in mind that some are very much more beneficial when paired with something else - like vitamin C and ferulic acid. The important thing is not to add anything that will further aggravate the skin, if it is dealing a defensive blow, it won’t be healing the acne outbreaks.
I hope at least some of these might help.