i'm not sure about the pain in the left side in her arm and leg but the headache and nose bleeds sounds are exactly what happened to me a couple years ago during the months when the season turned colder and the air was drier i started getting severe nose bleeds and even bled out of one of my eyes i honestly thought i was dying so i went to the doctors and found out my sinuses were the cause they were pretty much dried out. my doc explained that the bleeding was a way that the body was trying to rehydrate them so to speak he had my buy some saline solution that you squirt up ur nose and after using that for a day or 2 i didnt have any nose bleeds now i keep a bottle in my medicine cabinent as a just incase.i'm hoping that helps you out a little bit
I think the paramedics were probably referring to posterior nosebleeds, which are more common in elderly people or those with high blood pressure. Older people's blood vessels and arteries lose their elasticity and flexibility, so this may be what the paramedics were thinking. However, I don't think it's reason for them to dismiss what is going on with your daughter. You said they checked her vitals at the ER, so I'm assuming her BP must have been fine and not the culprit. On its own, I wouldn't think that the nosebleeds, or even the blood in the eye would be THAT alarming, but the pain on the one side of her body seems a little bit suspicious.
Pain on one side of the body would make me think of a clot, but generally clots result after injury, and to rest more assured, she would likely experience confusion, changes in her mood, slower thinking, etc., which it doesn't sound like she has. I've gotten the run around multiple times with general practicioners, but I've found that ENTs do tend to take you more seriously, and have a lot more knowledge about these types of issues than regular MD's. I hate that I have no advice for you, but if something does happen between now and Monday there is always the ER. Also, have you contacted any providers with an ENT on staff to find out if you absolutely need a referral to the ENT?