I stopped moisturising about 1 month ago and I now I only moisturise when my skin actually feels dry, which turns out is very very rarely. At first I felt really bad and weird about not moisturing since its like a textbook rule for skin care and I've always moisturised after cleansing as a habit. But since ive stopped I have noticed my skin is much less oily and sticky (which it used to be even hours after I had put just a tiny bit of moisturiser on) and much clearer. So I would give it a go. I've not had any problems with giving up moisturising, but thats probably because my skin is so oily. I do occasionally put it on before I do heavy makeup but thats it. Good luck

I'm going to let you in a little secret. Fruit face mask. Add all types of fruits in it (banana wil moisturizer your face) and blend it up, put it on your face for 30-1hr. You'll be surprise how your skin will look from one application.

Try using a moisturizer without any active ingredients in it - simple moisturizers are just way less likely to clog your skin.

How does your skin feel right after washing? Does it feel tight - like you can feel the stretch when you smile? I think in general moisturizers are good for skin, especially in POC b/c we get ashy. Also if there's a lot of dead skin hanging around, it combines with oil and causes breakouts. So you can have dry skin + acne. The two are NOT mutually exclusive.

Your skin also looks like clogged to me. You could try some gentle exfoliation. I really like the Paula's Choice products. The Ordinary is also good -- it's cheap skincare you can get online so you could get a BHA or AHA from there.