After a bunch of trials from several different tutorials on SSH, I got it to work on my local network (easy), then, to finally figure out why my port forwarding configuration on my router wasn't working: my ISP uses CGNAT, which means my public IPV4 address is actually shared and what identifies me is an IPV6 address, so that's why port forwarding doesn't solve any problems.
Now that part of the problem I got figured out: I found out about ngrok and now I can access my SSH server from outside my home internet, tested it on my phone's mobile network with ConnectBot app through the tunneled address provided by ngrok. I can access my server on my home network using PuTTY both providing the local address and the ngrok address.
The problem is that, when I try to connect through PuTTY from my university PC, the connection times out which I assume is a sign that the connection is being blocked. I assume that they block ngrok addresses and not SSH connections in general but I could be wrong.
Maybe one option would be trying to connect ssh using my IPV6 directly but I have no idea if this is possible. Also, I should try to connect to a "standard" SSH server to try to figure out if the university blocks SSH connections, but I have no idea how as well (don't know any place to connect).
Any thoughts how to solve this?
PS: At home I can access my university lab PC through TeamViewer and vice versa. TeamViewer VPN doesn't work tho.
UPDATE: IPV6 does work on PuTTY when I use the same PC that is hosted the server. The android app doesn't seem to support IPV6 tho, so I can't test on my mobile network. When I try the same PuTTY configurations but on my university's PC I get a very fast error: [PuTTY Fatal Error - Network error: No route to host]. All my other attempts took a long time to give me an error, but this one is instantaneous, so it seems IPV6 might be blocked altogether.