I love first person myself. I write in it all the time (like now! )

I probably write in first person POV more than any other, so I ponder stuff like that a lot.

Usually I'll use something like, "I felt my cheeks burning" unless I am feeling particularly clever, in which case I'd use a more clever bit of prose than I can think of off the top of my head. (Sorry, I stared at the keyboard for two minutes, time to move on.)

I read a lot of 1st person as well, and I think you're just fine with "blushing" in private. Words are communication with your reader above all else, you don't always have to put flowering prose on the page, sometimes you just need them to know the character is blushing. Sometimes there are more important things to spend your word count on.