I don’t think hydrocortisone cream is what you need. What you’re describing sounds a little like eczema but may just be a result of your allergies, as you said. I suggest you try this stuff first for a few weeks and if it doesn’t get better you may want to see your doctor.
“This stuff” is Aquaphor Healing Ointment. You can get it at Walmart, CVS, Walgreens, etc.
A 2-pack of the small-sized tubes is only about $5.00. Here’s the company’s website which shows all of their products: https://www.aquaphorus.com/use/dry-cracked-skin/
And here’s an Amazon link: https://www.amazon.com/Aquaphor-Healing-Ointment-Advanced-Therapy/dp/B00BS7A5JA