I am attempting to connect with my database that's situated inside a server with a lot of other databases (that goes with other people who are on a single webhost).

Because of my low internet speed once i connect when i click growing databases more often than not I recieve no results waiting.

It is possible to way will be able to filter databases that only would load my databases disregarding others?

Consider denying the server permission VIEW ANY DATABASE to yourself or request the server's DBA to get it done.