I wouldn’t recommend it. You’re going to feel shitty enough without adding fasting on top of it. Personally, I think you should eat. I only lost my sense of taste and smell for about a day and I think the reason for that is because I Was trying to smell and taste things; I was trying to exercise and activate my olfactory senses lol. You do you but I’ve been there and I’d say don’t do it.
I got sick a few times upon fasting just because I started at points where my body was quite weak. Having had covid twice, I can easily say your body will feel it’s worst (-ish, at least.. but hopefully not!). Covid will pass soon, eat & drink your vitamins till then. Feel better soon!