The lovely College nurse is there to talk to at specific times if you're feeling a bit poorly or need any kind of minor injury fixing up. Her room is just off the far Fawcett staircase on the first floor.
All Newnhamites are registered when they join the college. This is located just behind college on Newnham Walk.
http://www.newnhamwalksurgery.nhs.uk/
It's not compulsory to register with a dentist whilst you are in Cambridge, but it makes life a lot easier if you get tooth ache during term time! A number of surgeries can be found in town.