Hi there,
You can use some of FileMaker's built in access controls to do this. Check out the section "How Do I Let a User See Only Their Records?"
here.This talks more about securing appointments, but you do the same thing for contacts.
Note that preventing editing is a little less intrusive than preventing someone from "seeing" a record: FileMaker is kind of ham fisted about that. If you do need to prevent someone from seeing things, consider applying field-level security so they can see the record, but not certain important information IN the record, like open balances, emails, or invoices.
Hope that helps,
John