I've always wanted to be a nurse, until I realized how much of a hard time I'll have dealing with death. Especially since I can't see myself not working with children. I still want to stay in the medical field, I just don't know what else there is. I was also looking toward speech therapy, I'm so confused on what I want.
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What do you do right now? Have you looked into pediatrics? If you're in school, I'd recommend talking with professors and counselors now, as there are many, many options in the medical field. If you're working, I'd try to get in touch with nurses who work at a large hospital, which provides a good variety of different specializations. LinkedIn is useful for finding people that way.
One thing to remember is that most nursing jobs, and especially those that deal with children do not require dealing with death and dying. A couple of examples are working in a general pediatrics unit or in a pediatric doctor's office.
Any of the "therapies" also would allow you to work with children and not deal with death: speech, occupational and physical to name a few.
As far as medical school is concerned, if you can get into a school, it's very unlikely that you will not be able to graduate based on an inability to learn the material. Once in, the schools have a vested interest in having you graduate and will do everything in their power (if you ask for the help) to get you through.
Finally, don't be scared. It's not the end of the world to start something and change your mind in midstream when you find something that's more interesting or more suited for your personality and abilities. Your whole life is ahead of you. Take it, experience it and laugh at what it throws at you!