Hi there!
So, for the past year I have been dealing with a bunch of issues. I went through a stressful time in my life which destroyed my skin. I was under a lot of stress and anxiety, my moisture barrier got destroyed, I started breaking out with large cystic acne, my skin was just super dry/dehydrated and broken out. It seems to be getting somewhat better, but the medication I have to take can cause skin dryness (oh goodie). I cant seem to quench my skin's thirst with any type of moisturizer because I am sensitive to literally everything I put on my face! Cerave, cetaphil, la roche posay, everything in sephora and ulta, NOTHING has worked. Ive tried natural products but they seem to put irritating essential oils and fragrances in their products so I can't use them. Baby products have not worked either. Anything with fragrance, acids, essential oils, extracts, parabens, sulfates, etc all irritate my skin. I still have some acne sores on my cheeks from 4 months ago because they simply will not heal because nothing will moisturizer my skin, everything irritates it. I simply cannot wash my face with any type of cleanser, literally everything leaves my skin feel stripped and tight. They absolute only thing that does not cause a reaction are certain plant oils, avacado oil, jojoba oil, and coconut oil (which supprisingly does not break me out). The only thing is, is that these oils dont seem to get down deep in my skin and hydrate well enough. Im still left with dry tight skin. I need a moisturizer of some sort but have ran completely out of options. I drink a ton of water, I eat pretty decent, I take my vitamins, reduced the anxiety and stress in my life but I am still reacting very negatively to almost every moisturizer out there. Please, if anyone has gone through this, could I get some advice. I havent been to the dermatologist because after reading online it sounds like they just suggest products that I have already tried and have failed to fix my problem and I dont want to waste money.
The skin needs both water and a measure of fatty content/sebum on the skin to keep it balanced. Oil and water is different so the plant oils can't really compensate for your skin's dehydration/lack of water.
Your priority at this point should be repairing your skin barrier. If you can, try leaving it alone for two weeks or so and just use a mild cleanser. In some cases, the skin can reset itself in time if left alone.
Mild Cleanser: Non-foaming (so it free of irritating surfactants), hypoallergenic, non-comedogenic, fragrance-free. Try VMV Hypoallergenics.
For a moisturizer, you can try Physiogel Hypoallergenic's Calming Relief AI Cream or Avene Cicalfate Recovery Creme. These are products that are specifically used to rebuild the moisture barrier by supplementing all the things needed for balanced skin.
You can try other products as well as long as it ticks off the four boxes above.
Good luck! 
