I'm the one doing the paper work but if my boyfriend is the one to claim hoh should I start over now and put him first or does it matter

Not sure what you are asking about.  If you are not married you each file as Single or one of you might qualify for Head of Housed if you have a qualifying child.   You each need to have your own separate online accounts.

The Online version is only good for 1 return. But you can use the same email address for 5 accounts. To do another return you have to set up a new account and new user name and pay any fees again. That's why it's better to use the Desktop CD/Download program. The Desktop program can do more than 1 return and efile 5 for free.

How to start another return in the Online version
https://ttlc.intuit.com/community/using-turbotax/help/how-do-i-start-another-return-in-turbotax-online/00/25596