Routing ALL traffic through VPS

I recently acquired a Raspberry Pi and I'm setting it up for various things. I have a local router that the Pi is wired into along with my desktop computer. I want to be able to access the Pi from outside my local network. I have access to my personal router, so everything works within MY network, but my router is plugged into a larger network that is locked down for obvious security reasons so I cannot access my router/Pi directly.

I have a domain through Namecheap that allows me to use dynamic DNS, and I have that DDNS working with my Pi using inadyn (set up on a subdomain). I also have a VPS running Ubuntu Server 14.10 which uses that domain.

What would be the best way to enable connections to my Pi over the internet? I want access to all ports and whatnot like normal. I started configuring OpenVPN on the VPS, but I stopped to ask this question here. Is there a way to tunnel my Pi's connection through a subdomain of my VPS and access the Pi using that subdomain (again, allowing access to my ports, e.g. pi.website.com:22 for SSH or whatever), or is there a different/better way to do this?