…I feel like the biggest goy by saying this but it’s a little uncomfortable….”
It CAN be uncomfortable. Why feel like the biggest ANYTHING, for simply expressing an honest view? There are many things we do l’shem mitzvah that may not be comfortable, i.e. sitting in the sukkah in cold weather. There is no aveira in saying you are feeling COLD. AS long as you do what you are supposed to do, you get the s’char mitzvah. Anyone can do a mitzvah when it is easy. the one who does it even when it is NOT easy, gets some extras brownie points. If you really feel uncomfortable, find a more comfy way to cover your hair. That is also perfectly ok.