A sub-question to this would be whether dolls count as golems. Alice's dolls aren't autonomous, so Shanghai is out. Medicine, however, may fit the bill as a Wood Golem or a Wool Golem, depending on what material she was made of.
Hmm... but with that reasoning, would every tsukumogami count as a golem as well? I suppose we can limit the definition to "being artificially created"? So people like Medicine and Kogasa are out because they weren't constructed, but born naturally.
But where does that put Aunn then? Her case certainly doesn't paint a picture of being constructed. I mean, sure, it's Okina's doing – but it's pretty much the same case as to how the tsukumogami got a power boost with the Miracle Mallet...