Flushing that occurs during menstruation

I feel like I get flushed on my face especially during my period.

Suddenly, my makeup doesn't apply well or cover blemishes, and when I reapply something, it feels stuffy.

My skin also gets hot, so I sometimes feel a sensation of heat.

I use a rubber mask to soothe it, but it comes back when I put on makeup.

I'm wondering if there is a product that can cover up redness a bit more moisturized in times like this.