I'm not sure how it is for Medicine, but for Dentistry, shadowing experience during high school does count, and you can put it on your application - I actually did the vast majority of my shadowing while in highschool, over 200 hours, and maybe only 10-20 while in college with different specialists.
And yeah, high school is a great time to start shadowing, because hell, you may turn out to hate dentistry and want to become a mechanic or something totally different. The sooner the better. Most dentists I've talked to are actually very open to students shadowing in their offices - (dentists often have a very strong sense of "passing along the trade" ) so just give your dentist a call, and tell him you're interested in dentistry, and if you could maybe stop by for an hour or so one a week or something like that. Though, as said above, some people just won't want to, and in that case, just open up the phone book or go on google and start calling dentists near you - and yes, it's a very good idea to shadow with specialists, but you'll really want to start by shadowing a general dentist.
Good luck!