I have a history of Prostate Cancer in my family. My grandfather died with it although not from it, uncle had prostatectomy and now my 82 year old father has an inflamed prostate. The doctors will be concerned when there is a big jump in PSA and yours is a big jump. I think you should have the biopsy done. My father had both a cystoscopy and a biopsy. He just has an inflamed prostate but due to the family history we are watching it. Most Prostate cancers are slow moving but it's not something to fool with and if something is going on whether cancer or prostatitis it will cause you to eventually start urinating frequently. This is a very common issue in males north of 70. FYI I am 57 and I run 1.3-1.4 on PSA consistently for many years but I anticipate issues once I get north of 70, assuming I make it to then.
Good luck to you.