I would say to the OP, that if you are at all bothered by bodily fluids then healthcare of any sort isn't for you, whether that is nursing, doctor, physio, whatever. Go do something else.
I've been a qualified physio for two years, and have worked in a big London hospital on a variety of rotations. I have just spent 6 months in elderly care and have the utmost respect for what the nurses have to put up with. However, as a physio, I too was elbow deep in vomit, excrement etc. The fact of the matter is that the nursing staff are so pushed that you often end up doing their jobs, and they sometimes end up doing yours. It is a big team effort. If I go to an elderly patient for some exercise etc, and that patient is covered in poo, urine, whatever, I'm not going to just walk away and let the nurses do the clean up when they get the time. Myself, the OT's, the HCA's and everyone else has a duty of care to that patient, and that means that you get your hands dirty. And as for doctors, well do you not think they get their hands dirty doing rectal exams, colonscopies etc?
The fact of healthcare, certainly in an NHS setting, is that everyone on the team gets stuck in. If you really are a germaphobe as you put it, don't go into any line of work involving caring for people.
As for intelligence, I can assure you that completing a physio degree, and I'm sure nursing and all the other allied healthcare professions is not an easy undertaking. As has been mentioned, the placements as a student are back breaking. I would work a 9-5 and then hold down 20 hours a week working a paid job, and then do essays and revision ontop of this. I am not over-estimating that my average working week was at least 80 hours, stretching upwards of 100 at busy times. If your heart isn't in it, you will fail.