It would be bad for my pores if I exercised without removing my makeup, right?

I've been going to the gym diligently lately to take care of my health and figure, haha. Since I head straight to the gym after work, I end up sweating without removing my makeup every time, which feels really uncomfortable and is a big concern for me. Removing my makeup at the gym's communal sink before working out is kind of a hassle... and I'm also a bit embarrassed to exercise with a bare face, so I just work out with my base makeup and sunscreen already on.

But when I exercise and my body heats up and my pores open, I feel like makeup residue and impurities are all clumping together and getting sucked right into them. It’s scary. Lately, whiteheads and blackheads seem particularly prominent around my nose and cheeks, and tiny bumps are popping up one by one. I wonder if it’s all because I exercised without removing my makeup, and I regret it so much every time I look in the mirror. I really, really want to hear some real-life tips on what kind of cleansing routine everyone else follows.