Spark plugs or coil pack issues are probably the most common cause of a random misfire. I would check those items, as they are often related to the symptoms you describe.
If you don't have a code for EGR, it is unlikely to be the source of your problems.
It's a relatively simple system, a single EGR solenoid controls exhaust gas flow from a port on the exhaust manifold to a port on the intake manifold, in response to a signal from the ECU.
Two common issues with EGR:
- Plugging of the intake port
- Failed solenoid not responding (or responding insufficiently) to ECU signal
Both of these failures are monitored by the ECU and should set a code if present.
Without a code, you can't really test for #1. Treatment involves removing upper intake manifold and cleaning the EGR port on the manifold and probably the corresponding passage on the lower intake.
The EGR valve is usually actuated on startup, so you can locate it and check/feel for movement on startup or you can apply 12v via a jumper and observe.
Hope that helps!