As you are so fearful of everything related to this, I would probably recommend a second opinion. This does not have to be done immediately even if you decide to have it. You can afford to give yourself a little grace. Breast cancer induces anxiety and if your doctor doesn’t have the patience to address your fears, maybe that isn’t your best fit of a doctor.
Every single thing is a risk vs benefit decision for us, and that equation looks a little different for all of us. I had an axillary node removal (all available). I did not have any pain from the injection of the dye with the tracer, and I didn’t have any pain from the blue dye when the machine was broken to track the tracer.
It did have the side effect of blue breast and inner chest area for months. My husband referred to me as Mrs. Smurf for a while.
Also just a reminder about online forums. The people who write the most are the ones who had a problem, very few people get on to complain that it was no problem.
Have you considered getting a second opinion? Do you live in an area with a large teaching hospital or a cancer center?

That injection was so painful, I screamed, burst into tears and jumped off the table.
That breast was already sensitive after two rough biopsies, black and blue breast and large hematoma.
I thought it was barbaric to give such a painful shot with no anesthetic at all.