Yes, the squeamish DO survive! The first time I had to change a dirty adult diaper as a nursing student, my partner ran out of the room gagging! I thought to myself, what'smatter, don't you have pets or younger brothers or sisters at home that you've had to clean up after? Anyway, she got used to it, and managed to graduate.
I was at a wound care conference recently, and just before lunch, they were showing all these lovely photos of stage 3 pressure sores. I had to turn away from the screen. Then I noticed a nurse at the table next to me had her head down on the table, and behind me, a male nurse was sitting with his head between his knees...These were all experienced nurses, too, not students! Somehow, when the wound is part of a living breathing body, it's easier to handle, because you're looking at the whole person.
I went into nursing late in life, and graduated at the age of 42, so it can be done! If you think it's the right thing for you, go for it! The only place you're likely to see lots of blood is in the ER, or the OR, so you can avoid those two areas if it upsets you.