Yes, they can track you. There is no way around it.
I assume that you’re not trying to do anything wrong, but I’ll just explain that I worked with a volunteer organization & we used to track down scammers/spammers all over the world. Tracking an IP can take 5 seconds.
Even if they used a proxy, there were ways to get their info (although it’s a little more complicated & a lot more time-consuming).
And public computers make it even easier to track down people. Internet cafes. Public libraries. It doesn’t matter, the people are on camera the second they walk into the place….