Their love is a close friendship. Amy and the Doctor have a very close friendship because of the fact he was her imaginary friend after he spent a few hours with her 7 year old self. She grew up drawing pictures of the Doctor (she still had these 14 years later) and playing dress-up with Rory where she made him dress like the Doctor.
Amy never loved the Doctor romantically. You may be confused due to the scene where Amy attempts to seduce the Doctor (See "Flesh and Stone") and tells him she wants him instead of Rory, her fiancé. Amy may have been confused for a few episodes, but before long it is proven that there in nobody in the world she loves Rory Williams.