Is an exfoliation treatment okay for extremely dry skin?

I heard that dead skin cells need to be removed periodically but shouldn't be too irritating, so I stopped using the peeling gel I was using and have been using only a foam cleanser and skin pads containing AVAHA. However, as I get older, it seems like the dead skin cells are increasing, and my skin texture isn't the same as it used to be. No matter how much I moisturize or use face masks, the texture of the skin between my cheeks and jawline is not satisfactory. I definitely feel like the exfoliation isn't working properly, as that area always looks patchy when I apply makeup base. As a result, I often end up replacing it with a moisturizer before applying makeup. That is why I would like to try a professional exfoliation treatment...

My skin is very dry—extremely dry! Is it okay to get an exfoliation treatment on skin this thin and lacking in moisture? I'm worried that getting an exfoliation might actually make it drier and even cause itching. If there is a treatment that can exfoliate dry and sensitive skin without irritation, please recommend it. Also, please advise on how often I should get the treatment, my budget, and precautions to take afterward. :)