Is it okay to work out at the gym after applying sunscreen?

hello.

The weather has been very hot lately, so I tend to sweat easily.

I'm wondering if I really need to wear sunscreen when I go to the gym.

It takes about 10 to 15 minutes to walk to the gym, so I do get exposed to sunlight while traveling.

But when I actually work out at the gym, I sweat a lot.
It seems like the sunscreen washes off quickly.

I'm also worried that my pores might get clogged and cause breakouts...

I've heard that it's not good to apply sunscreen or tone-up cream when exercising.

(Exercise > Sweat > Blockage of waste elimination)

It is an indoor gym, but it is on the 4th floor and has large windows, so quite a lot of sunlight comes in.

I exercise for over an hour, so I'm also worried about UV rays.
So I'm really conflicted about whether it's better not to apply it or if I should.

By any chance, how do you apply sunscreen when you exercise?
Is it okay to wear sunscreen even when going to the gym?

This is a photo that captures my feelings...