How to handle well-meaning clingy-ness?

Hello, hopefully this is the correct sub for this. I am a woman in her early 20s and started my first semester as a freshman this month. It has been going okay so far but I do have one issue.

On my first day I made friends with another person who is a lot like me in many ways, we have similar demeanors/interests/thoughts about stuff. They are a few years younger than me though and they haven't left me alone since the first day we met. Like, if I even go to the bathroom they will follow or stand outside level of clinglyness. I haven't had much of a chance to make friends with anyone else and I am kinda hesitating to because I know for a fact they would be right behind me or next to me (silently and kinda just waiting to interact with me or the conversation I am having).

Most of the friends I have had over the years were very similar to me in every way but I am kinda done with that. I want more extroverted friends, people with different hobbies/interests and ways of interacting with the world. I don't want to get stuck babysitting someone as or even more anxious/insecure than me and missing out on new experiences I want to try. They seem lovely and I am open to still being friends but not like, to this level.

But I don’t really know how to handle this situation without hurting feelings or making them even more insecure than they already are. Them being this close to me is frustrating cause while I know I am not their babysitter- I also know myself and I couldn't go to a social event they followed me to without feeling like I need to stick by them the whole time.

I would love to hear if other people have had this experience and what you did or would do in this situation.