Welcome. This is Jim. This is a great place to learn.
The correct use of PSA is tracking of annual values rather than using a single value as a "cutoff". Example: For men < 40 yrs, the "cutoff" at Johns Hopkins was 1.8 ng/mL The cutoff of 4.0 ng/ mL was established without any clinical assessment of the men involved. In truth, one would have to take out men's prostates and step section them to establish they are "normal", which is close to impossible. Having said that, I tracked mine for 30 yrs and it slowly rose to around 1 as my prostate also enlarged. Then the hiatus of my healthcare system denying routine PSA. Before the "pandemic", it was 2.0, A year later it was 4.0 (I was allowed PSA as a professional courtesy). No action was recommended because it was "normal". A year later is was 6.9. That got my doc's attention. Diagnostic MRI sees a lesion. MRI-guided 12 core biopsies reveal cancer in 10, eight of which are Gleason 7, but two being Gleason 8, i.e. high risk disease. PSMA PET sees no signal outside the prostate (but I don't think the detection limit is known).

So, now the dilemma: radiation vs prostatectomy. If all the disease is in the prostate, prostatectomy is a cure with very manageable side effects. The main factors are your general health and age, and access to PSMA PET. In my opinion, a healthy man in his 50s - 60s with low - medium risk pathology and negative PSMA PET is a good RP candidate. However, I swung toward radiation for the following reasons: Improvement in avoiding radiation side effects. I had access to MRI-guided radiation which minimizes likelihood of radiation damage to colon and adjacent structures, and is completed in five days versus thirty. I also had access, prior to treatment, to Hydrogel placement. This gel serves to separate the colon from the prostate. In my case, my large prostate was pressing against the colon, so this was a key to my success: no urinary or intestinal changes.

One caveat. Many radiation patients are recommended to take androgen deprivation therapy such as Lupron, starting 2 months prior to treatment, and continuing for a total of 18 months. It drove my testosterone to zero in 3 months and PSA to 3, and then to zero three months later, but everyone hates the side effects of Lupron. I agreed to this because, regardless of the surgeon and radiation oncologist's optimism, I know something about prostate cancer and pathology. Given my high risk pathology, I would be very surprised if all of the disease is confined to the prostate. Lupron/anti-androgen is for me a low-tech insurance policy. It is claimed to "slow" the growth of prostate cancer. Perhaps. I have not seen the data. However, it is not curative.

Back to you. I would not be concerned with PSA 9 vs 11. I would be extremely concerned with both. Do you have prior values such that you could look at the trend? In any event, how was the biopsy done; how many were taken; what were their pathology? I would not act on a single needle biopsy. Next, you didn't mention your age or general health. I look at radiation as taking a bit of a roll of the dice: are you likely to die of other medical problems before any missed cancer would have a clinical effect? In my case, when my surgeon (original doc I saw) called to tell me about the pathology results (I had already seen them), his first words were: "the good news is, you won't die of prostate cancer". Well, he probably felt somewhat secure in saying that since he knew I was 80 yrs old. However, he knew nothing about my overall health, which it happens, is extremely good for any age, so he made some assumptions. I was not reassured by his statement. I hope this starts to get you back on your feet after your news.