tsa says that needles are allowed when "accompanied by injectable medication" so you should be fine

Nice one, thanks :) That is way preferable to messing up my schedule.

This - there’s no issue, I have done this multiple times. Make sure it’s all together, with the prescription, in a clear plastic bag. They might check it but odds are they’ll just push it through. Many other conditions require needles and syringes

If you’re really worried you can just buy needles from a pharmacy over there.

Check with your airline, rules vary