I just got new contact lenses. My previous prescriptions were: 

4.50 - left eye
3.25 - right eye

Now, my new contact lenses are:

3.25 - left eye
4.25 - right eye

My right eye is perfect now. But my left eye, is very blurry. When I
pop in a 4.25 or 4.50 into my left eye, my vision is perfect again.

Is this normal? Does it take some time getting used to? The reason my
left-eye dropped was because I went to an eye doctor for the first
test, then my second tests were done with my regular eye doctor.

How long ago was the last prescription (4.5 L and 3.25 R)? It is
certainly odd that your prescription would change so much in just a
year or two unless either 1) something is going on to damage your
vision rapidly, or 2) there was a mistake in your prescription. I
would do the following:
 - confirm with your optometrist or ophthalmologist that the
prescription was written correctly
 - confirm that when you said that "5 is better than 6" at the office,
you were comparing between 3.25 and 3.5 for your left eye and not 4.25
and 4.5 (which is what it sounds like)

Unless you have comorbid conditions (e.g., diabetes, hypertension,
glaucoma), vision shouldn't change between your appointment and trying
the new contacts at home. Contacts can certainly take some getting
used to, but this is usually related to their comfort and not how
blurry your eye is (unless it was dilated recently at the office and
just hadn't recovered when you asked your question). Regardless, I'd
certainly go back in--you shouldn't be charged for a return visit if
there was a mistake.

Good luck, and please let me know if I can help more.

--Brendan--