There's a package named Support that you should install from Package Manager. After it's installed you'll have a new link in the ADMIN page, named Support Assessment. Follow the link to a page presenting a report about the environment OTRS is running on. The report may load VERY slowly and return timeouts. Keep retrying. When it finally succeeds, go through it and beware of any anomalies as they may clue you into why you're having problems.
Additionally, notice that on the Support Assessment page you have a link in the upper left named SQL benchmark. Follow the link to a page from which you can run a benchmark on the database. This will help evidencing if there are issues for OTRS with the connection between the web server and the db server.
If I understood things correctly, you have the db server on a dedicated machine (call it dbsrv-machine) but you run the VoIP server on the same machine as OTRS (call it websrv-machine). In this case, an additional thing to check would be if the Apache instance running OTRS is starved for resources (memory, etc.).