Access to the different interfaces of TeamDynamix, and the permissions you have to do things within those interfaces and applications, are controlled by two things. Firstly, your security role on your account, and secondly by the applications you've been granted access to.
A person with the "Client" security role can only access the client portal and the applications/sections available within it.
Then you have a handful of other security roles that all have the Technician license or above which can be used for provisioning access to users that need TDNext access (in combination with the application access that you specifically grant them).
I don't see your name on your school's implementation project that just wrapped up recently, so you might not have received the training on administration that those folks involved received. You might check in with them to learn the best way to administer user access.
Sr Support Consultant, CS