I have not had an iron infusion (the IV version of iron), but I have had an iron injection and I am happy to describe that experience if it will be helpful.
To start off I will point out that I had a form of anemia that doesn't respond to oral supplementation and that it took me about three years to convince a doctor to actually bother giving me an iron injection to address my continuing symptoms. I also have B12 deficiency. The injection I received included 1ml of iron and 1ml of B12 injected into my hip using the z track method (a method that keeps the iron from causing a permanent stain/tattoo at the injection site). (Z track method is not needed for iron infusions which is one of the reasons infusions are more popular than injections.)
The injection itself was about as painful as an injection normally is, however soreness at the site lingered for about a week and caused an adhesion (I think that is the word) which feels like a lump at the injection site. It has shrunk with time (I had the injection about 2 months ago) but is still there.
It took about two weeks for me to actually feel a benefit from the injection (which makes sense considering how long it take the body to generate new blood cells). When it really kicked in, I felt increased energy and no dizzy spells or weakness for the first time in a long time. I was told at the time of the injection that I might need another one to get my levels to a good place where they will hopefully stay. I've been a bit reluctant to book another injection because my symptoms haven't become as bad as they previously were and those injections do actually hurt.
Obviously an infusion is a bit different. You wouldn't experience an adhesion from IV iron so you probably wouldn't have as much lasting discomfort as you would from an injection.