These two words are not interchangeable.
IMPLY means to suggest without overtly stating something: Heather implied she might go out with Jason if he took better care of his teeth. (What she might have said was something like, “Jason is really cute and I like him, but his dental regimen needs improvement.”)
INFER means to deduce, to figure out: Jason inferred that if he brushed his teeth regularly Heather might go out with him. (Someone might have mentioned to Jason that Heather thought he was cute but was turned off by his scummy teeth.)