I agree, see a doctor. If you're already eating 5-6 meals a day, you shouldn't be getting hungry in between meals that often. There's no reason a completely healthy, active individual, who's eating proper meals, should need to regularly eat more often than every 3 hours. Sure, we all have those days where we feel like we're constantly hungry (or at least I do), but they're the exception. Walking a few miles a day isn't going to do this to you. Even professionals training for marathons, running 50+ miles a week, usually don't eat more often than about every 3 hours, which means 5-6 times a day.
If the docs give you a clean bill of health, I'd look at what you're eating at meal-time, because if you're healthy and hungry this often, that means your meals just aren't cutting it. If you're genuinely hungry, and losing weight (and have no other health problems), you probably need more calories in your meals. Also, as was mentioned before, try drinking water. Dehydration mimics hunger in a lot of people and can certainly make you feel faint and shaky. If you're just getting strong cravings for junk food, maybe you're depriving yourself at meal time just a little too much. It's okay to indulge a little. A few bites won't kill you, or make you fat, just make sure you really pay attention as you eat them, really taste them, so it satisfies the craving without causing a binge and making you feel sick. If you're really concerned about your teeth, make sure the vast majority of liquid you put in your mouth is water. One of the worst things otherwise healthy people do to their teeth is sipping on soda, juice, and even milk throughout the day. If you must drink these things, try to do it at meal time. Drink water after to rinse your mouth every time (or even better, brush your teeth, even just with water).
Some great snacks with staying power (pay attention to serving sizes, Don't go crazy):
Savory/salty
Nuts- healthy fats, protein, fiber
Full-fat cheese - fat and protein (several studies recommend eating full fat cheese, just stick with lowfat or skim for actual milk)
Hummus- protein, fiber, healthy fats (make your own in the blender, so you can be sure to use EVOO and avoid all the processing additives, it's super easy and a simple google search will yield tons of recipes) Dip veggies, pita chips, even plain tortilla chips (watch your sodium, though)
Sweet:
Ricotta cheese with fruit preserves, honey, even a drizzle of chocolate sauce (if you use it as a dip for a graham cracker or 2, or crumble one on top it's a lot like cheesecake, but still considerably healthier)
Cottage cheese or yogurt (especially greek) with above-listed toppings
Bananas
Fruit combined with cheese/nuts/other protein source (otherwise you'll be hungry again nearly as quickly as if you'd eaten candy)
high-fiber muffins- I love banana, zucchini, apple, pumpkin, or butternut squash muffins made with whole-wheat flour, or even extra bran/flax/etc
Keep in mind that none of these things are healthy if you eat too much of them. That's why they're snacks, not meals.
Good luck with everything!