Hi Chema.
I had a trans rectal biopsy and before the procedure they gave me a dose of antibiotics to help fight any possible infection. Obviously they are puncturing your prostate capsule so there is always going to be a possibility of infection arising.
Im not sure but I think TP biopsy might leave you with a bit of discomfort when sitting so a flight so soon after might need a bit of pain relief.
I can't say if it will be more painful than my TR biopsy but with a local you shouldn't feel much anyway. Just relax and let them do their job. The only thing I felt was each time they collected a sample but really it was nothing.
Good luck with it and just rest up if things are a bit sore.
Also be ready for blood in your urine and semen. It looks quite scary but it's just a part of it. The urine clears up pretty quick but the semen can take some time.