90% of people who have oral hsv1 never get a cold sore, so you can have it and never know.
Given that you tested at 5-6 weeks post-exposure (possibly), there is no way to know if this is a new infection, or one you've had for a long time. Most people will develop antibodies within 6 weeks.
So you have to figure out if it really matters (hint - it does not). Medically, it makes no difference, and emotionally, it shouldn't either. It's just a virus that you (and millions and millions of others around the world) have.
A note though - there is no such thing as a herpes carrier. A carrier implies that the virus is in your system but dormant, or inactive. What we know about herpes is that even without visible symptoms, it can still be active on the skin, which is called asymptomatic viral shedding. It is possible to transmit it when this happens. Since it's asymptomatic, we don't know when this is happening.
However, don't freak. Many people have this, and if they already have it, they can't get it from you again. You aren't shedding every day. You CAN transmit this to someone's genitals if you perform oral sex on them, especially if you do so when you have symptoms. (Again, if they already have hsv1, chances of this happening are very low as they have antibodies. Just don't perform oral sex with an outbreak, and include this in your STD discussion that I'm sure you have with partners lol.)
HSV1 is discussed in the Herpes Handbook - https://westoverheights.com/wp-content/uploads/2014/08/Updated-Herpes-Book.pdf