Before doing any gaming, open either Task Manager or Resource Monitor. Use both tojols but only one at a time.
Watch what the system is doing and/or does - first without gaming and hopefully with no overheating or high temperatures.
Then, leave the too window open to one side or the other and play Valorant. Again watch what the system is doing and for any changes in resources, apps, etc. that cause the temperatures to increase.
Consider that the laptop may be running other apps etc. in the background and that adding the load of playing Valorant may be "too much".
Look in Task Manager > Startup for apps, tools, utilities, etc. that may be being launched at startup: for example - backups, AV scans, updates. some utility software. Or some app simply trying to "phone home".
If nothing is found or otherwise discovered then take the laptop to the University's support center. Hopefully they will be able to troubleshoot the laptop.
In the meantime, as you always should be doing, ensure that all important data (projects, classwork, notes, reports, and so forth) are being backed up.
You should have at least 2 x backups to locations off and away from the laptop. Verify that the backups are recoverable and readable.
Remember if the laptop or SSD fail in some way then all could be lost.