So azelaic acid is used for treating both rosacea and breakouts. As a previous poster recommended, The Ordinary do an azelaic acid which a lot of people find really effective. You could start there and see how you get on with it. Another option for you could be Dermatica - a brilliant prescription service which I use myself. You upload photos of your skin and they’ll formulate a product for you. They use azelaic acid and also other ingredients which help with breakouts and acne. It’s £20 a month but I spread mine out to receive every 56 days so it ends up being £10 a month as I never go through one bottle in a month! All the ingredients are prescription strength so really effective!
So Dermatica is definitely an option to consider but if you wanted to try over the counter products first then azelaic acid and salicylic acid are 2 ingredients which would work well, you may also like niacinamide! I’ll happily recommend some products and/or a routine for you if you like!