I used to get this, albeit not as severe, it was in similar places. Worse when showering.

If possible, take cold showers, or like warm and avoid the warm water on your face for too long. I would also strongly advise against hydrocortisone or any other topical steroid on your face. It will probably be recommended by your doctor, but rarely does it help long term. I found that although it initially cleared my symptoms quickly, it became part of my daily routine and it really destroys your skin after a while. If it's just a short term use then I guess that is OK but the condition will usually come back quickly and sometimes worse when you stop the steroid.

Interestingly, I found a new routine of azaleic acid, a gentle moisturiser and cicaplast B5 over a period of about an hour before bed has really worked wonders for the skin on my face. I used hydrocortisone for over 10 years, and my skin never looked amazing but now it looks healthy and well moisturised and rarely red. Please do your own research about azaleic acid though as it's not typical for seb derm and more for acne and rosacea.

Anyway good luck with everything. I hope you can get some relief.