Would it be beneficial to get two PRP injections 1 week apart?

I am guessing the doctor had excess PRP that was not used. So he/she froze it and wanted to inject more - that is where the free treatment most have come from. Since redoing PRP has $$$s to the doctor. Best to ask why free???

Great question. It does take time to see the results from PRP injections under the eyes. Although multiple sessions usually work best for the undereye area, one week apart seems like a little too soon. A recent review of 19 separate studies using PRP for the under eye area (Evans 2021), showed intervals of between 14 - 56 days between treatments. The most common seems to be every month, but in my experience there seems to be a better long term effect by having treatments a bit closer together, e.g every 2 weeks. I would like to know more detail about the type of PRP that was used, e.g. system, single vs double-spin, concentration, and was it tested for concentration, purity and dose of platelets prior to use?