I wouldn't worry, I think most people go through it to a certain extent. I used to get it a little during dissections but now (finishing my biology degree and having done a lot of med work ex) I'm totally fine with it.
A doctor I was shadowing in cardiology told me a crazy story about one medical student he had who fainted: he was stood watching a coronary catheterisation and as blood arced out of the radial artery he fainted straight backwards and hit the concrete floor head first, out cold and having to then have his head x-rayed and sutured... But even he got over it so I'm sure you'll be fine!