Just guessing but you may have mistaken the "1 chance" to make recovery discs from the OEM installed on the system. Vendors like HP or whatever used on, provide the pgm. whicj allows a 1 time use. However, once the recovery discs are made can be used repeatly on the same system. I just can't recall any 1 time use of an OS install limit. As explained to you by other posters, the EULA allows re-installs if you have the recovery or orginal discs for same.
You need to check HP support website to see how, the recovery process is accesssed if one is found on the HD itself. It does vary from model to model or series. Likely F10 or F11 during boot-up and the menu should be explained. Again, to be certain, HP provides that info for your model#. Otherwise, if you already have access to recovery/OS install discs make sure the bios is set to boot from CD/DVD drive as 1st device and proceed.
If possible ask your school IT or any helpdesk if they provide such info.