Global only scoped trace flags in MS SQL Server
If the scope of the trace flag is global only does it mean I can't use it only for one connection while not affecting the performance of others?


The scope signifies the affect of trace flag, a global scope means it will be applicable to all connections of SQL Server, it cannot be made to work only for particular connection/session. On the other hand trace flags whose scope are limited to session will be applicable to particular session.

If you refer to Trace Flags documentation it says


  Trace flag behavior may not be supported in future releases of SQL Server.


If you are using SQL Server 2008 and above you have extended events to get deadlock information. Please see 


Getting historical deadlock info using extended events
Graphically Viewing Extended Events Deadlock Graphs