You are probably getting an allergic reaction, I agree.
You shouldn't need or want to wear heavy makeup. Foundation makeup is the most important of all. That's why they call it foundation.

Call a nice dept store that sells Estee Lauder cosmetics. Tell them on the phone that you are transgender, you're under medical care and you are beginning your transition. Tell them you would like to buy some foundation and ask them if they'd be willing to help you. Tell them if they are in any way offended, you'll be happy to go away and try another store.
I'm certain that you won't have to call too many places before you get a very sympathetic ear and someone with expertise in makeup who is very willing to help you.
You want to buy Estee Lauder Double Wear foundation. It will cover virtually anything on your face, it will literally wear all day long and you'll look terrific. It costs about $50 a bottle, but it lasts forever.
The single most important thing about foundation is to match it to your own skin tone. If it matches, you can't tell you're wearing it. You can buy cheap stuff all day long and end up spending a lot more than just getting it right once.
I ride a bicycle in the Summer and I've had sweat running down my face, where it was difficult to see and when I was done, my Double Wear was still there. I just went swimming and it survived nicely.
Not too long ago, I was at the cosmetics counter and the lady asked me if I was wearing foundation makeup. Then she said, "oh, no, you're not wearing it today..... are you?" Yes, I was and I was blown away by how good it is.
Walgreen's drug store sells makeup remover wipes in packs of 25 that will take it right off at the end of the day.
My points are simple--it's not against the law to shop for, and buy, cosmetics. Many of these women professionals will love to help you. Calling ahead will help you set up an appointment, so the fear can be reduced. The only way to get good foundation is to have a pro match it up for you.
You may need to also buy a concealer if your beard is super heavy.
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