There are many ways to filter traffic by process in Fiddler; a simple search on any major search engine will turn up all of them.
For your needs, however, you simply don't want Fiddler to be the system proxy. Hit F12 or untick File > Capture Traffic; no other client will then send its traffic to Fiddler.
If you only ever care about requests from the Composer, click Tools > Fiddler Options and untick "Act as System Proxy on Startup" on the Connections tab.