Blood test to investigate infection after rhinoplasty?

An ENT thinks I could have an infection in my nose after revision rhino using my own rib & ear grafts. He asked me to get blood tests. I am wondering how accurate the blood tests are? Am worried because my nose is dripping on one side and feels delicate (absorbable stitches were used). I had a bad reaction from the last lot of antibiotics so I don’t want more. Also my throat was bad 2 days before surgery and I coughed a lot of phlegm after surgery could that have caused an infection in my nose?