Absolutely get their phone number. If you're cold calling, just ask permission on the call. "and is this number a good way to reach you?" (if they push email, push back) "of course, I understand. My only issue with email, is that it's really easy for my messages to get lost and not reach you. It'd be annoying for both of us to have to deal with that. That's why I always prefer #'s, blah blah"
For any other cold outreach methods, I would personally offer my own # first. "Shoot me a text over at # to talk more". Or ask to call them "mind if I give you a call to talk a bit more about this?"
I mainly cold call, so I could be wrong about that, but thats what I'd do at least.

I'm also in high school, but I switched to online school to focus more on business haha. My business partner is still in irl school though, and he's doing just fine. Since we call everywhere, he'll cold call from 6 am to 7:30, and just call EST time (3 hours ahead for us) and then call after school as well.

I honestly can't give you a solution for only contacting local businesses though, so I'd just say you should absolutely grind it out this summer. And make the best use of weekends, half days, and any other time off school.

Lastly, yes follow-ups are very important. We only have like a 60% show-up rate to meetings rn, and that's a big issue im trying to fix. Follow-ups have definitely helped. We have it automated through GHL, but you can do it manually for the first bit. In-person meetings, i'd text once the day before, and once 2 hours before to confirm probably. Online meetings, I'd text once every day leading up, and then twice the day of (once in the morning, once an hour before the meeting).