Welcome to our Forum.  thanks for your confidence in our service.  I'll do my best to help. Before I address your specific questions, I'll first comment on your continuing concern about HPV and why realistically, this is not something to worry about. 

If you have read our replies to other clients, you are aware that our science-based perspective starts with the fact that virtually all unvaccinated, sexually active adults have HPV and that in more than 99% of those persons, their infection will cause no lasting problems.  In less than 1%, if undetected the infection may progress to readily detected pre-cancerous lesions which can be readily managed with regular sexual health check ups and management by health care professionals. Thus HPV infections are not something to invest a great deal of concern in.  Visible warts are an observable manifestation of HPV infection, primarily caused by two HPV types which are from a health perspective, little more than a nuisance since they almost never progress to pre-cancerous lesions.  Since you have received the HPV vaccine, you can be confident that you are protected against acquisition of new HPV causing genital warts.  Unfortunately many health care providers are poorly prepared to distinguish HPV from other benign dermatological processes like molluscum contagiosum, skin tags, and scarring from part folliculitis and all too often treat them with non-specific, destructive treatments which may make the lesions go away but do little to address any fears that their patients may have regarding what he lesions are or where they came from.  My guess is that this may be the case for you.  Since you were vaccinated, the lesions that were treated are most unlikely to have been newly acquired warts and if it has been more than a year since your earlier lesions were evaluated, are also unlikely to be recurrent HPV either.  (Occurring at the base of the penis, they are also an unlikely location for genital warts which are far more common on the shaft of the penis)

With this as back

1)  Since the bumps were frozen off,  should I still try to get a biopsy or wait to see if there is a recurrence?

No, properly applied cryotherapy is a destructive process designed to destroy the lesion.  There is little to be gained from a biopsy at this time. 

I hope this information and perspective are helpful to you.  EWH

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In your expert opinion what are some tips or some best treatment options other than freezing the warts off?

There are a number of ways to treat visible warts.  If a person (or their doctor) is unsure of whether the lesion is a wart or not , a biopsy is often both curative and diagnostic.  In addition to freezing, other effective treatments include laser.  While more time consuming, there are self-applied treatments which include imiquimod and podophylin.  EWH---

  Your responses are very helpful!  This concludes my question and you may close this case.  Thank you doctor so much!

Thanks so much.  I'm pleased my comments were helpful.  EWH---