If it makes you feel any better, I totally cry like a baby when I see movies, touching commercials, anything like that. I never did until I had my daughter, then it was like some switch in my head was turned on. While I understand it's embarrassing to be the person crying, I think there are enough of us in the world that no one will really hold it against you.
I don't really have suggestions, the previous posters had some pretty good ones. I would, however like to share a story with you.
Last year, in my senior term of my BSN program, I was required to participate in several shadowing experiences for one of my classes. Long story short, I shadowed in a NICU for a 12 hour midnight shift and was able to see the delivery and immediate intubation of a 23 weeker. It was extraordinary, in so many ways. I have never felt so touched and awed by what we are medically able to do until that moment. The father came into the room where the NP, nurses, and neonatology fellows were all working, and the charge started asking him questions (she was very, very considerate and knew he was pretty overwhelmed). The look on the father's face, as he watched what was going on with his daughter, and the questions...I'll never forget it. It was so much to take in and I just felt myself beginning to lose it. I held it together long enough to leave the room with the charge, but then just burst into tears. No one mocked me, no one looked like I was doing something embarrassing. The charge gave me a huge hug, as well as a few of the other nurses, and told me that they would have would have been really shocked if I hadn't reacted that way, being new to the NICU. My Mother works on the unit, but wasn't in that night. I don't know if they ever told my Mother that her 29 year old daughter sobbed on their unit or not. I do know that she wouldn't have cared. She's shared with me many occasions when she's just had to cry because of something happening at work. She has cried with parents, she has cried with other nurses.
You'll get used to seeing things, both horrific and wonderful. But sometimes, something will touch something so deeply in you that no matter what, you just need to let out the emotion. Don't be ashamed, and don't let anyone try to make you feel that you should be.
And BTW, deep breathing and thinking of something completely unrelated do help me when I'm tearing up at something really corny, like a movie or a hallmark commercial.