I sent a text message to a girl I didn't catch up with, but she said she didn't save my number and asked me who I was. Is it necessary for me to contact her in the future?

Maybe she really didn't leave your number, but it's more likely that she doesn't want to talk to you. Let's not contact again. Let nature take its course, if you can still be friends, you will naturally have the opportunity to contact in the future. Keeping in touch now may make her dislike you, which is counterproductive. It's better to calm down for a while.