I am not a psychology specialist, but I can give you a brief outline of what they are for (don't worry, we Brits have a similar issue with the professional bodies, especially in healthcare).
BPS - the professional body for psychology related professions. I would make sure your undergrad is accredited by this body to do anything related to psychology.
BACP - this is the regulatory body for therapists.
HCPC - this is the regulatory body for general health professions.
BPS, BACP, and HCPC should all coincide and give you similar information on anything related to the psychology professions. In terms of bodies to look at first, I would prioritise BPS, HCPC, then BACP.
If you have a PGCE that has QTS, then I can't understand why you're not a teacher (the country is facing a massive shortage of teachers at the moment).
I also am not entirely sure what specific role you intend to go into when you say "my goal is to work in schools and work with kids". This could mean anything from being a teacher (which you should be able to do with your qualifications), become a child psychologist, therapist associated with children of some description, or a nursery worker.
If you want information on the roles avaialble, see the following:
https://nationalcareers.service.gov.uk/job-categories/teaching-and-educationhttps://nationalcareers.service.gov.uk/job-categories/healthcarehttps://www.careerpilot.org.uk/job-sectors/childcare/job-profileshttps://www.careerpilot.org.uk/job-sectors/education/job-profileshttps://www.careerpilot.org.uk/job-sectors/therapy/job-profilesIf you can be more specific, then I should be able to help narrow things down.