I'd hardly think that you have problem skin! Haha but it looks to me like you just have larger pores! I would look up ways to try to shrink them and maybe use a lotion that tightens the skin. Even if you have to go and get a anti aging lotion just find out what products are best for large pores that won't clog your pores and cause more break out.

Have you tried tazorac, some type of retain a?

That could help with yr skins texture

just don't pick while yr on it

If you want something to nourish yr skin

Try a lotion with bio oil in it or bio oil by itself, but for some ppl it might cause breakout but it's cheap like 10. Bucks just try it

Try leaving yr skin alone and just wash with purpose wash (dermatologist recommended) and moisturize

But if you decide to try something strong I recommend retin a even though u don't like to exfoliate

use a retain a and add a moisturizer to it