It is not a problem to use a self-signed cert provided that you distribute that cert to users so that they can verify that the cert they are approving is the cert for the genuine site and not some site spoofing it. In this situation, you are told to approve it but you have no way to validate that you are connecting to the correct site.
So there is definitely a risk for accepting it. If someone was able to create a fake site, put their own self-signed cert on it, and somehow convince you to go there (via social engineering, DNS tampering, WiFi attacks, etc...), you'll approve a cert for the attacker's site and never see that warning again. Then you'll happily pass your credentials to that site. Very bad.
What you need is to get the fingerprint of the actual self-signed cert then compare it to what your browser is seeing (see this page for reference). But I'd guess that you will have a hard time getting any more information from the site's owners. So you have to decide if you are going to take the risk or not. One way to lower the risk a bit is to try to make the initial connection when you approve the cert happen over a more secure internet connection. For example, a hard-wired connection is likely harder to be altered by an attacker than a WiFi connection.
Depending on how the site is configured, you may be able to connect to it, approve the cert, login with your school id, then immediately change your school password (best if from another browser altogether). That will reduce the window of exposure if the connection is being snooped. Hopefully the site will allow you to stay logged in for subsequent accesses so you don't have to do this every time.
In the end, you'll have to get more information about the cert so that you can verify it by hand or cross your fingers and hope for the best.