Yes, all of your internet traffic can be tied directly to your computer.
Can they identify you personally? Your Wi-Fi adapter communicated to their network using its own MAC address, so they can tie all the activity coming from that MAC together. So any one thing you did online that identified you personally, such as logging in or entering your email address, could be used to link your identity to your entire browsing history.
A different question is whether or not they are monitoring and/or recording your traffic. Most schools will route your traffic through a filtering proxy of some sort; these proxies may provide a report of violations to your school.
They may normally not trace your connections, but if they discover you are using their connection for something illicit, they will likely examine their logs more carefully for evidence of who the computer belongs to. But those are guesses as to how they may react; your results may vary.
If you are concerned, there may be some things you can do.
If you did not install a certificate provided to you by your school, then as long as you connect only to https sites, they will only be able to see what server you connected to, and how much data you exchanged, but not the exact contents of the data. If you did install a certificate, they can intercept everything you are doing.
For better protection you can use a VPN tunnel, which will protect all of your traffic from interception.