Let it go...
and observe what's going on. You aren't qualified to do anything other than that anyway. Practice your vital signs, ask is you can help take a BP and pulse. Watch and learn how the crew you're assigned to works up a patient.
If you're lucky, you'll be with people who want to help you learn, if you're like me, you'll end up with one crew that each took some "personal" time at their respective family and boyfriend's house, note, if you're gonna stop off at the boyfriend's for a "quickie" tuck your shirt back in before you walk back out to the ambulance, while on the clock and another that didn't really do anything, well we went to the grocery store for a while...
Ironically, the crew that I did my first ridealong with, spent more time standing by or "posting" but were much better at showing me the ropes and teaching than were the other two combined.
As for the ER, watch the nurses, they run the ER, contrary to what most doctors think. Show them that you're interested in learning and they'll teach you, goof around or sit back and do nothing, and they'll probably let you do that too. Realise that while you're new and everything looks exciting to them, it's just another day at work. Try to find the people who are still interested in what they're doing and go to them for help.
Like the ambulance ridealongs, you won't be qualified to do much in an ER setting so whatever jobs that they do let you do, learn from them. Talk to patients, try to remember that they all have a family, that they're not a commodity to be "treated and streeted".
Good luck.
John E.