Pink eye and FMLA

Would pink eye fall under FMLA? I have pink eye and a terrible, painful sinus infection. I’m missing work more due to the sinus problem cause I can’t eat and it’s so damn painful but obviously I don’t wanna spread pink eye. The dr confirmed both today I don’t wanna use vacation as myself and kids have been sick a ton this year so far and I have used up a good chunk of vacation. My other option is FMLA. They’re a pain in the ass to deal with. If they approve my two days off I nee I wouldn’t get “points” or use vacation. 3 points and you are fired but if I try for FMLA I can’t go back and use vacation. I already have one point due to being late for work because of th bad roads.