17-year-old got credit by accident with NEXT, now at 22 can't get any kind of credit

R34GTT

If I had to guess at the issue it would be this:

The first credit history alias generated for your name and address would be with your false DOB from your Next account. It is probable that subsequent credit searches were throwing an error due to the discrepancy between your real DOB and false DOB at your original address.

However once manual checks were done you were approved by Virgin at a new (student) address with correct DOB which would create a second alias.

You then moved and applied for Natwest at a (new?) address and correct DOB. If you didn't supply your student flat or original home address as a previous address then no link would have been made and hence yet another alias, the third one would have been created at the new address (or are you back at your original home address?).
This is why your old accounts are not appearing.

If you check your credit files now with the current address that matches the one Natwest have then at least the Natwest account will or should appear. The Virgin one would probably appear the next time you apply for credit if you include your student flat as a previous address (assuming this is the one Virgin used). The Next account will never appear as it is hiding in your original alias with the false DOB. You can safely ignore the Next account but it is because your first interaction with the CRAs was with a false DOB that initiated the problems. It is also possible that if you are at your original address again or using it as a previous address in applications that the false DOB is again causing automatic declines as that alias is the first one for your name at that address.

I think from now on you'll be fine, just check that Natwest is on your credit files now. It may be worth contacting the CRAs to explain the problem and see what they suggest if you continue to have problems.