Yes, SSL/TLS use port 443 by default. Is this port allowed? If you can check gmail or online banking then it is supported.
The most recent HAK5 video (Dec 17) showed an SSH tunnel. The default SSH tunnel is 22 - this will likely be blocked by the offsite Firewall filter. You can keep the ssh listen port at 22, but map the local 22 port to 80 on the public side (on your SSH server's WAN Firewall).
So if your SSH server resides on your home LAN, on your firewall, open public port 80 from the WAN side to port 22 pointing to the LAN IP address of the SSH server. THen setup DynDNS.org on your router's DNS update client or whatever.
You can then use Plink or PuTTY Tray to open a SSH session to your personal SSH server and set a loopback port (Hak5 used 9999 in video). Then configure your Web Browser and other clients proxy settings to locahost or 127.0.0.1 and port 9999 and enable SOCKS 5.
If you use Firefox, get FoxyProxy extension and be sure to also check "DNS requests are proxied as well".
There is another way of doing this without an SSH client session running (this assumes port 443 or HTTPS is not disabled offsite). You can install a personal Proxy Server and Stunnel (SSL server) on a computer on your Home LAN. Squid and ProxyTunnel are two that come to mind
http://squid.acmeconsulting.it/
Configure Stunnel to redirect WAN traffic from the listen port 443 to the LAN proxy.
Then configure your Offsite webrowser to the WAN address and port of your proxy. No SSH client is needed, but this only works for HTTP and can't be configured for POP, IMAP etc ... without separate servers running.
Of course, if you can not change your web browser's Proxy settings then you're SOOL