@usernameunlocked I would bet your first intuition around needing a domain name is correct.

I’d recommend:

1. Buy a domain name (NameCheap has a bunch of the new extensions for as cheap as $2.88/yr)
2. Point it to DO nameservers
3. Add the domain in control panel and point it at the Droplet
4. Use nginx as a reverse proxy on your Droplet so you can map HTTP ports to your internal service’ port 8989 (just in case your school is blocking requests that use non-standard ports)
5. I doubt it is the cause of the block, but you could also setup Let’s Encrypt to get HTTPS for free

Hope that helps.