As you know, you cannot request response from one or the other of us so you are stuck with me. 

You raise a number of questions and may be unclear on some of the scientific facts regarding HPV infection. I'll try to address them below. The first question is whether or not you have genital warts.  You do not mention when you noted these bumps following the sexual contacts that you describe above.  Further, it sounds as though you may have two different processes- one which you describe as "small skin tag looking bumps at the base of my penis" and a second solitary process that is somewhere on the shaft itself.  (It would be unusual for genital warts to appear in tow different places with different appearances or to appear in less than 2-3 months following sexual contact). There are a number of cutaneous condition which can cause genital lesions including actual skin tags, molluscum contagiousum and other processes.  Thus, for this reason, I would endorse your decision to have someone else take a look- perhaps a dermatologist or STD specialist if you have access would be best.

Second, the fact is that you have had at least one other sexual partner and perhaps your newer partner has as well. If so, my suggestion would be to assume that one or both of you have HPV infection, whether you know it or not and to not worry about it.  Since at least 85-90% of sexually active persons have or have had HPV, far wiser to assume that you do than to worry about whether you might have it on not.  If you make this assumption, then the next issue is what to do with/about your HPV infection and most experts would say: 1. as long as men have suspicious lesions evaluated and women follow reproductive health recommendations ( for PAP smears, etc.) to prevent the RARE consequences of HPV so that they can be treated, unless there are cosmetic concerns, there is little to worry about.  Treatment can be worse than allowing HPV infections to resolve on their own as most do. and 2. If visible warts become a concern, have them treated with the easiest, least expensive treatment available.  Further, if you really believe that neither you nor your partner have HPV and perhaps even if you do, the widely available HPV vaccine almost completely eliminates the risk of genital cancers and dramatically reduces risk for further infection.

Finally, there is no data to suggest that hand to genital contact or rubbing ("grinding", even with wet clothes), leads to transmission of HPV.

Yes, the data on clearance does include genital warts.

I hope this information is helpful to you.  A second opinion will be helpful. In the interim, please try your best not to worry. EWH

As I mentioned above, in all likelihood your partner either has been vaccinated or is already infected, whether she knows it or not.   Transmission estimates are difficult to calculate.  There are of course no guarantees but the odds of you infecting your partner are small. AT the same time, your concerns are laudable and one approach would be to discuss your concerns with you partner. This could clear the air and when people are able to do this, it tends to strengthen relationships.   EWH