Get a new phone number and never sign it up on anything. It is very easy to replace a phone number. If you have had a phone number for multiple years and signed it up multiple times and still using it, it is time to change it now.
Blocking somebody on social media doesn't really mean anything, they still have your account, can still see your posts, comments, and even liked videos if they use another account. You would have to delete your account if some random person has your personal Instagram that you don't want anybody knowing, even if it is private.
They both have there downsides though.
How old are you? Nobody uses email for regular chat