Got flu shot on friday. 36 hours later sore throat and headache. no fever . could this be immune response to vaccine?

Most likely immune: Most likely it is your immune system responding to the flu vaccine.

Probably UNRELATED: A flu shot might cause a little temporary soreness at the shot site (that's where one feels the body's response). A sore throat and headache most likely would be caused by cold viruses, strep throat germs, allergies, etc... Whether or not a person just got the flu shot. Having the shot and getting the sore throat are likely unrelated coincidences. A doctor may check the sore throat for strep.

Coincidental: Flu shots rarely cause side effects nowadays. You would have got it regardless of the flu shots. When i recommended vaccination for shingles to one of my elderly patients , the patient declined only to develop a case of shingles 2 weeks later. She would have blamed the shingles on the vaccine had she obtained it.