Now when you say strands, are you talking about "high-risk" (cervical dysplasia kind) and "low-risk" (genital wart kind)? The only HPV test that's normally used can only detect that. Now, I have heard rumor that there is some test that can tell you exactly what strain you have (example: HPV 16, HPV 11, and so forth). Thing is, I don't think it's something that's used stateside. I have heard someone from the UK getting it, and she found out she had HPV 45. I thought I read her saying it was available over there, but here they don't use it. Again, don't quote me on that. Just what I've heard/read.
Now, say you only knew that you had the "high-risk" hpv. Never showed signs of "low-risk". That doesn't mean, just because you never showed any signs prior, that you weren't already a carrier. It's not uncommon for people to carry the virus without any symptoms whatsoever. You can still pass it of course. You could've gotten it prior to your new boyfriend. Could've gotten it from the same place you got the "high-risk" from. People can obviously carry more then one strain of the virus. Then again, it could be possible that your new BF gave it to you. It's really hard to say for sure. I've heard people having it dormant in their bodies for a loooooong time, and then suddenly, out of the blue, get symptoms.
As for reinfecting, that's a hard call. There have been several recent discussions on this topic you may want to look back on. First off, opinions vary on if the virus actually is cured from your system, or if it just goes into remission. I've heard of people clearing symptoms for years, and never having another problem again. Yet I'll hear of other people who'll clear symptoms, and then down the road have them pop up again. It's often thought, if a couple is sharing the same type of HPV, that they can't "ping-pong" it back and forth. Once it's in your system, it's in your system. You're not going to "reinfect" each other. Now some couples, if one is having symptoms and not the other...even though they share the virus...will take precautions until the symptoms pass. Using like the condom/boxer shorts method. Then other couples figure screw it, what's the point when we share it, and don't worry about it. Now if your partner is infected with a different strain of the virus then you currently have, then yes, they can pass that on to you as well...like I previously mentioned, you can get more then one strain.
It's all very confusing, I know. Like I mentioned, there's some previous discussions on this kind of topic you may want to look back on. You can also check out this site's HPV info section, if you haven't:http://www.ashastd.org/hpv/hpv_learn.cfm