Yes, they will check "down there." They may do an ultrasound
as well--those are always fun! They'll likely want a blood sample, too.
Look, if you're uncomfortable, find yourself a gynecologist or a general practitioner who is a FEMALE. Quite frankly, I SWEAR BY female gynecologists AND doctors for female patients...they're more gentle, they do sensible things like warming the speculum (nothing like an ice cold
device up your hoo-whee to make you tense and nervous) and since they HAVE the equipment they are examining, they have a better understanding of your descriptions of how things are feeling "down there."
Are you underweight? Do you have an eating disorder? Are you terribly stressed? Or (and I know this is unlikely in the extreme) are you pushing fifty? All of these reasons can cause your period to stop.
Another thing that can cause your period to stop is simply premature menopause--it's not common but it does happen.
Please, get the phonebook, ask around, get a referral from a trusted friend, but do find a doctor and get yourself checked. Like I said, unless you are well into or past your middle age, you should be menstruating, and the reasons you aren't could be something very straightforward, or something VERY SERIOUS.
Don't muck around now--get your courage together, and make that phone call. Believe me, doctors have seen THOUSANDS and THOUSANDS of "lady businesses" and yours will not be the first, or the last, or unusual to them in any way. I urge you to get over your reluctance, and pick up the phone, please!
I know you'll be happier-- once you're all through a bit of embarrassment and discomfort --that you did.
Best of luck--be strong, now!!