I'd recommend trying out the aztec clay mask with apple cider vinegar, it may leave your face red for a couple hours after application but it often draws stuff like this to surface as it sits and them gently breaks it open when I rinse the mask off in the shower with a hot wash cloth.

I do recommend removing it in the shower and pressing the hot face cloth to your face to slowly break down the mask so it doesn't clog your drain coming off in chunks. The benefit is also more of a hot compress which again helps you from having to actively press these to get the trapped cells and pus out which reduces scarring.

I did also find a lot benefit to the Eradikate by Kate Somerville, it has sulphur in it which has been useful in drying out tough spots on my face. And as someone else mentioned you should cut out dairy as a starting point, I am lactose intolerant and my regular acne crops up on my chin when I consume even small amounts of dairy (think cheese slice on a burger even).