Nicole, don't ever worry about that 'intuition' thing; and don't ever worry about the 'every little thing'. You're the mom. YOU - drive the care of your family, not the doc. If you're not satisfied with the answers you're getting, go somewhere else.
Nosebleeds in toddlers are NOT the norm. It may in fact be something very minor, but you're not going to know until somebody who's really qualified checks it out. I'm glad you're taking her to see an ENT, a specialist in 'ear, nose and throat'.
While we're on the subject, this is good advice for everyone here. We as a population have to get over the 'doctor as god' image. We all have to drive our own care, and represent ourselves as part of a health care team, not lemmings who blindly follow someones' advice when it may seem contrary to our own 'instincts'.
I've had more experience with the health care profession both as an employer and as a family member, especiallly with my son's accident and resulting spinal cord injury six years ago. We've had some top notch care for him, but we've also had care I wouldn't wish on my pets. I could tell you stories about the times I've gone head to head with 'know it all' ER personnel or nursing staff, because they weren't dealing with an issue I knew was important.
On the other hand, the docs we've found who have accepted that we're a knowledgeable part of a team have been a dream to work with.
Trust yourself; do your research; and take care of that cutie!