Hello Chiara,
It is possible to use MATLAB activated with same license in different operating systems on the same computer. For more details, you can check the following link: https://www.mathworks.com/matlabcentral/answers/97198-can-i-use-the-same-matlab-license-in-different-operating-systems-on-the-same-computer
The error that you are getting is not because of multiple MATLAB installations. Since you mention that you are using a university license, it could be a username issue. Check out the following links, it might help:
https://www.mathworks.com/matlabcentral/answers/99067-why-do-i-receive-license-manager-error-9
https://www.mathworks.com/matlabcentral/answers/246774-license-manager-error-9
Thanks