I've check all my settings, my phone is not in Do Not Disturb mode, but I cannot get my alert sounds (messages, phone calls, etc) to work. Only vibrate works. Toggling settings off and on does not work either.
If you can't play music either or listen to voicemails (to check the receiver and the speaker) then you have a hardware or software issue.
If you can play music and listen to voicemails, then you have a software issue or a configuration/setting mismatch with what you want the device to do.
Hardware issue - usually starts with eliminating software issues, but in this case observing the headphone port for damage might be a great quick fix.
Software issues, back up the device and test after restoring it and verifying the settings.