looking for proxy or tunnel for https traffic

[Vivent]

Not sure if I'm putting this question in correct category, but let's go.

I am working on project on uni, where we need to write a web app and deploy it on server that we got from uni. Let's assume that the url where our project is avaible is https://projects.uni.com:8403. My group bought a cheap domain to make it easier to get to that app, because the url is long and not convenient to type it. For now we're using nginx (npm) server on my unraid server for redirect us to app/admin panel based on the sub domain. But we thought that it would be really nice if we could proxy all the traffic that goes to our domain through the unraid server and to the uni's application server.

How do I do that? SRV record not working, nginx not working, and I don't think SOCKS is gonna do what I want
srv record that I've tried:
test IN SRV 1 1 8403 projects.uni.com.

nginx proxy that I've tried:

I tried to install shadowsocks container, but looking at the avaible config, I don't think this is what I want.

 

I just want to proxy all the traffic from point A to B. Is there any easy way to do it? The certifacate on the uni's server is self-signed

[Vivent]

With the help of the professor, I figured out the IP for the domain (any dns lookup couldn't find it for some reason). So now We have a nice domain by just setting up "A" record

 

The "figuring out" was to just ping the domain BUT from the internal university network.