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I have generally oily skin in my t-zone and areas where I am affected by redness. My skin has been reacting pretty heavily to the wintertime climate but I don't know how to diagnose this? Can anybody explain to me what the inflamed, red, crusty patches of skin are on my cheeks and nose? the first picture is about 30 minutes after sweating and a shower. The second is about an hour after I woke up 
Yes it could possibly be, my face looks similar except not as red but its still slightly tinted. I was diagnosed with Seborrehic Dermatitis last week, you may want to do a little research into it. Have you been to a dermatologist? He or she would probably be able to give you a quick assessment and diagnosis pretty quickly.
I have not been to a dermatologist in awhile but plan to make an appointment soon. I was trying to see if anyone on here could help with verification first. I also think it could be seborrheic dermatitus as I sometimes get flare ups of that under my nose, the corner of my mouth and the eyebrows. This is more inflamed though (which is hard to see in the pics) and seems different. Plus I have never had seb derm occur in those ^ ares of my face. What did the derm prescribe you?
A couple of conditions can co-exist with each other. My sister has rosacea along with mild acne and I have seb derm with mild acne so there must be a genetic component. Do any other family members have skin conditions? My derm gave me an antibiotic named keflex for the acne type spots, and a 2% Nizoral shampoo with the key ingredient Ketaconazle to use on my scalp and beard area. Since he suggested this I am finally convinced that he agrees that my acne type spots may be yeast related.
There are sub types to rosacea.
It does look like a reaction to me. Did you use a new product. Or scrub too hard?
Or you mentioned cold weather and sweating and showering.
All 3 of those together would cause increased blood flow.
I hope that is all and that you don't get rosacea. It sucks!
Only problem with head and shoulders is the other harmful ingredients it contains like sulfates. The only reason head and shoulders works is the active ingredient-Zinc Pyrithione, is known to treat Seb Derm. There are way healthier soaps that contain the same active ingredient but less harmful ones that I have tried and had mild success with. They got rid of the Seb Derm but the rest of my skin couldn't handle it.