Dunno why you said the "I'm saving you to my contacts" its ok just dont do it again.
The girl telling you shes grabbing tampons and is on her period or even beating around the bush is actually a good sign, she has some sort of comfort with you. She coulda lied and said something like deodorant, toothpaste, etc but she didnt. Plus she texted you first right? You're doing fine.
Its like if you ask a girl what she's doing and she says "trying on bikinis, getting a wax, etc". Would a girl say that to a random person, like her lab partner?
Anyways, just continue speaking to her like the way you got her number. Do some school orientated shyt on campus to show you're fun just none of those quirky lines like "Im gonna save you to my contacts lol", well unless shes weird and quirky, is she?
Good luck.