Nope, the needle they use is thin enough that if there wasn't an inflammation, any pain would be minimal (think how long the puncture site hurts after a blood draw.

What hurts is your immune system reaction to the vaccine or it's components (adjuvants) itself, because that's necessary for immunizing against the antigen.

Because you don't want something immunogenic circulating in your bloodstream. That's how you get cytokine release syndrome, shock, and dead patients. You want localized immune reaction somewhere safe (like an arm), where immune cells can be recruited to from blood , tissue, or lymph; to do their thing.

Seriously?! I had no idea! Is there an article I can read on that? I've taken basic immunology, but that wasn't covered.

Because you don't want inflammation response to vaccine speading through your blood stream and causing inflammation all over your body. That's how you get cytokine release syndrome, go into shock, and die.

You want a vaccine to cause a localized inflammation reaction (somewhere harmless, like an arm), recruit immune cells there, have them sample the antigen (vaccine), find ones that bind to the antigen, cause their proliferation, and as a result develop immunity to the disease. Your immune cells have a mechanism to be recruited out of the blood, lymph, and surrounding tissue and to get to the location of inflamation. Vaccination utilizes this mechanism. Vaccines are also specifically tested to work only through their specified method of administration, whether that's intramuscular (like most vaccines), nose spray (like flu mist), oral (like rotavirus), or skin administration (like BCG). Spraying regular flu vaccine into the nose won't work, just like giving it orally. It's formulated to elicit correct immune response only when it gets properly administered. The reason for this is more complex immunology.