You can try some simple tests:
Shut off the iPhone. Restart.
Are there any visible cracks on the screen, or bright/dark areas?
Open a few apps with icons that are in various parts of the screen (will tell you a little about how the screen is responding to touch)
Try the camera, with both closeups and distant shots to check for sharpness of the image. Take pictures in both bright and dim light.
Record audio to test the microphone, and to test the speaker for crackling/distortion
Call someone, ask them to call back, to make sure the phone function seems OK.
How about dings or scrapes on the surfaces and edges of the iPhone? Probably doesn't affect any operation, but might help you decide if you want to pursue any kind of repair. If there is visible damage, and you purchased AppleCare+, you might pay for an incident to repair or replace the iPhone... You would contact AppleCare then, who will make arrangements to pickup, or send you a shipping box to send to a repair center.
If those basic tests are good, your iPhone is probably OK. No visible damage?
The iPhone is good, move along with your life. (Your local wireless carrier, or a phone repair shop, etc, might also be a good place to take your iPhone for another opinion. It's a second (or third) set of "eyes" might see something that you are missing.