Will upgrading prevent my streams from loading in 360p?

Server Version#: 4.74.1

I have a handful of things on my Plex Server running off my desktop and it’s more than powerful enough to encode everything, I didn’t have this issue on my home network but here at college with multiple routers I can still access my Plex Server from another spot on campus but I can only seem to load my content in like 360p. I don’t have access to change or edit anything network-wise, but I was wondering if I purchased the lifetime plex pass if this would fix my issue or not, as with that you can stream your content from anywhere so I figured it has to right?

You are most likely in a multiple-NAT situation, which as you are describing it cannot be resolved.
Therefore you are most likely experiencing the restrictions of the Plex relay connection.
This is restricted to a bandwidth of just 1 Mbps.
If you get a Plex pass (life time or monthly), this will be only upgraded to 2 Mbps.

All devices here on campus are capped at 30Mbps for upload and download.

Sorry, this info bears no importance for your use case/issue.