Doctors and nurses use this kind of expression when asking about a patient's symptoms. For example:
Have you experienced any shortness of breath?
Have you experienced any trouble urinating?
The doctor or nurse can also ask "Have you been experiencing any ___?" for symptoms that are ongoing, like:
Have you been experiencing pain in your lower back?
A patient can also speak this way toward the doctor:
I've been experiencing some memory loss.
And finally, you can use "experience ___" for other problems that are not health-related. For example, on an airplane:
Ladies and gentlemen, we're experiencing some turbulence. Please return to your seats and fasten your seatbelts.