Don’t worry, you can setup those things for free.
I am quite sure you are running your own internal dns solution in your institution, so the name resolution part should be easy to cover. Just add the domains you want and point their a-records to the swarm cluster. In your home environment you can still use pihole or unbound to cover the dns resolution part, and use the organizations dns server in the target environment.
When it comes to Traefik. You don’t necessarily need to use Traefik EE. The free version is usually sufficient. You don’t have to use Traefik, you can create your own reverse proxy with nginx or apache. Though, personaly I like that it works very reliable with Traefik, as it doesn’t have dns caching issues that you might experience with self created reverse proxy rules on nginx or apache.
So the only cost you have will be the time you invest.