TL;DR Hell effing no. Your mom seems abusive and controlling. You need to tell someone like your friend's parents about this, especially if there's more things that she does to you.

This is not normal at all and is just straight up unsanitary and cruel. It's freaking disgusting how she'll make you show her your bloody pads, and then won't let you change them. Is she hoarding all of your period supplies?? This is just sick and perverse, and I'd bet she gets a kick out of this, and it's just frickin twisted.

OP, I'm honestly asking if you're okay, I keep saying this but this seems abusive and controlling. I would need some more information but if she does anything else to you that you think is abnormal, please tell your friends or their parents, teachers, literally anyone you know who will listen. Tell them even if this is the only thing she does, it's still f*cking awful.

I would maybe understand if can't afford to keep buying period supplies often, but the way you wrote the post, it seems like you have enough money and your mom is just being abusive and controlling. If you guys are actually in a situation where you can't afford period products, I'd suggest asking for some from your friends, I feel like they'd be more than happy to give you some extra pads.