Okay, first: PLEASE BE CAREFUL using hydrocortisone on your face. It can cause a breakdown of the skin and indent scars if used too much. Google Seborrheic Dermatitis for confirmation of this.
I have Seb. Dermatitis that started as Angular Cheilits (cracks in the corners of mouth) and then moved onto my face. I tried everything from Apple Cider Vinegar to prescription stuff, but the only thing that worked on my dry, sensitive skin?
1. Wash face with a soap-free, fragrance and color free wash. Use lukewarm water and PAT dry with a towel. I got a sample of Dermalogica Special Cleansing Gel that's been a godsend for my poor skin. Email them and ask for a sample cause it's $$$. Can be used on the whole body.
2. Use a washcloth and hand towel dedicated to your face. Don't share with anyone or use on any other part of your body.
3. Cover the area with a natural anti-inflamitory cream called Florasone. It replaces cortisone and can be used as long as you need it. Non-irritating, too.
4. If you truly have psoriasis or dermatitis, the infection could be due to a fungal/bacterial infection. You know what my doc gave me? CLOTRIMAZOLE. Yep, the kind used for athletes foot. Get some generic at the drugstore or Target and apply morning and at night before bed to the areas. Works wonders after about a week. (After a few weeks, if it doesn't work, doc said try Lamisil or another fungal cream.) The moment you think you're cured, use it for two more weeks because your skin can have a rebound effect.
5. Face cream morning and night? Burt's Bees Radiance Night cream. It's non-greasy and heavy, just don't use too much. Also, it didn't irritate my face. Whatever you use, make sure it's unscented, for sensitive skin, non-comedogenic and has as few ingredients as possible. I can also suggest ALBA Aloe & Green Tea oil-free moisturizer as a great face cream that won't irritate.
As with anything, your mileage may vary, but I hope this helps. I know how frustrating all of this is.
P.S. - all derms recommend Eucerin or Cetaphil, but I've found them to be crap. They have mineral oil and stuff in it that's not good for skin. I'd switch.
Also, for the body eczema, you might try organic extra virgin coconut oil on your skin after the shower. It's natural, has anti-fungal props that can help heal ezcema and can be found at Whole Foods or other groceries for about $6-$7. Wouldn't put it on my face, though. ;)
Got seborrheic dermatitis in early 2009 and spent most of the year in the doc's office, scouring the net and self treating. My face is back to normal now.