I mean I wouldn't. Going to sound all superior and haughty here, but I feel it's kinda cringe. Either people post informative stuff on their pages (which, to be honest, I'm not going to social media in the first place to seek out) or it's TikTok cringe dance stuff. Let's not try to glamorize something that isn't exactly glamorous to begin with. But you do you. I DO follow one page in particular, but that's because he posts some epic, hilarious memes.
If you want to follow other dental students, by all means. Just create an account and follow them; you don't have to make your own account be dental-related. As for following schools, I'm assuming it's because you want to research stuff about them before an interview, perhaps. But once again, like the example above I made above, social media should be your last place that you're looking at. And even if it's not, the pages will probably be public. So again, create an account and go visit their page.
As for "cool" stuff you've seen during shadowing, what exactly would you post that wouldn't violate patient privacy? Genuinely curious here. My first healthcare job, we weren't even allowed to bring our phones into the OR. At my first duty station, we had to stop bringing our phones with us in patient care areas because
someone took inappropriate photos. Unless I was using the OMFS' DSLR to take photos during LeFort cases, I don't take photos with my phone when patients are around. Call me paranoid, I won't deny it, but I genuinely feel uncomfortable being in an area with lots of PII around and having the camera function on my phone on.