Hi flyted and welcome to the Board!
It’s easy to see where that rise in PSA in the light of your family history would grab your attention! I hope you “just” have prostatitis again, which I think is fairly likely but by no means excluding the chance that there is prostate cancer.
That PSA pattern could represent infection/inflammation alone, or in combination with BPH and/or prostate cancer. While that “free PSA” result is in the range that suggests cancer, free PSA, like PSA, is heavily affected by infection/inflammation; in other words, it is not reliable when the patient has a prostate infection. Given your personal history, another round of Cipro seems a no brainer to me; if the PSA plunges, then the chance for prostate cancer drops a lot. If your PSA does not go down, then there could still be infection/inflammation, just with a cause that does not respond to Cipro, as is often the case.
My father also died of prostate cancer, though he was in his 80s. While having a “first degree” relative – a father or brother – who had prostate cancer, especially one who died of it at a young age increases your risk quite a bit, prostate cancer is by no means in 2018 your father’s brand of prostate cancer. Survival has improved greatly, and treatments with related management technology are vastly better.

These days survival at 10 years from diagnosis, averaged for men with all degrees of seriousness, is virtually 100% - the best of any major cancer, with the few unfortunate men diagnosed with widely spread disease about the only ones at substantial risk of death from prostate cancer in the near term. (And even their situation appears to be improving.) Even at 15 years, survival compared to age-matched peers is about 95%!

(I appear to be in fairly good health at age 75 and with 18 years as a survivor of a once life-threatening case unde my belt.) This modern survival snapshot contrasts to the 1970s when about a third of all diagnosed prostate cancer patients didn’t make it to even the five year point.
One of the many improvements is genetic testing, which has made its way to the clinic in the past few years, though its use is still not widespread and it is steadily becoming more useful. With your family history, a genetic test panel would probably be wise; results can aid in therapy selection, though mostly for folllow-up therapies, if needed, rather than primary radiation or surgery. There is no doubt that we will see substantial advances in the usefulness of genetic results in the coming years.
If your results are still troubling after another course of Cipro, the next step might be a multiparametric MRI instead of a biopsy. This is becoming popular. I just posted about that on another thread on this Board. If it were me, I would not jump to a biopsy just yet; on the other hand, that is not unreasonable if it will give you peace of mind.
Good luck!