I am allergic to 99% of commercial moisturizing products. I do tolerate a few ointments, lotions are out because they usually contain preservatives which I am allergic to, plus the water and alcohol in lotions is drying. Plain old Vaseline, an ointment is safe for me and most. I also tolerate Aquaphor, but it does contain lanolin and many are allergic to that.
Mary Kay is a toxic stew. Since you have reacted to lotions I assume you are seeing an allergist or dermatologist and have you had or requested the 5 Day Extended Patch Test? Google this test. I've had the True Test Kit twice now. Medicare paid for this test and the kits cost about $1,500/ Not all allergists or derms are licensed for this test, so be sure to verify this before you make an appointment. Turns out I developed Allergic Contact Dermatitis in middle age. Products previously safe for me cause reactions and will for the rest of my life. You may simply have mild allergies, not causing papules or rash, and only suffering dryness but you are irritated and you clearly have some form of dermatitis besides your rosacea and psoriasis.
A lighter form of petroleum than Vaseline is Elta MD Moisturizer, pure petroleum which is extra refined and will soak in better in a few hours. It's all I use on my face. Expensive but lasts a long time if just used on your face and neck.
Only use a simple bar soap. Most soaps, especially soft soaps contain allergic additives. Grandma's Lye Soap, a bar soap is simply lard and lye and the lye is converted to glycerin in the soap making process, so you only are washing with 2 moisturizing products which clean you. It's a benefit to have soft water as you get more lather.
Kiss My Face is a another great soap, it's simply olive oil and glycerin, both moisturizing.
Are you on antibiotics' for your rosacea? My husband has had chronic rosacea for years but it is controlled with a daily light dose of antibiotic and if he has a flare which he will get because he spends a great deal of time outside, then he takes a full dose for about 1 1/2 weeks to calm it down.
I hope you are not using a steroid eye cream. I developed Perioral Dermatitis, which causes dryness and irritation around the mouth and eyes because of a steroid nasal spray was prescribed. Rubbing my face must have transferred the steroid. Then the dermatologist simply assumed it was my Allergic Contact Dermatitis and prescribed a steroid cream for around my eyes and around my mouth which caused a greater reaction. I self diagnosed the Perioral by using the website, dermnetnz.org, which has the greatest collection of skin condition photographs in the world, an amazing site. I asked the derm if this could be Perioral and she said, oh yes probably and I explained that if it was steroids trigger it and took me off the steroid topical. I discontinued the steroid nasal spray but it still took about a month for the burning, redness and itching to calm. That was over 8 years and go and haven't had a return of this condition. Just be aware of the negative side effects of steroids, yet in many cases they do provide a beneficial treatment to certain skin conditions, but they are only a treatment and not a solution.