Scurlock/Andersen in their Diagnoses in Assyrian and Babylonian Medicine (University of Illinois Press, 2005) call pašittu a type of disease:
The Akkadian term for cholecystitis appears to have been pašittu. Pašittu is lexically equated with bile, and the Sumerogram (ZU.MUS.I.KU.E) indicates an associated severe pain.
They cite the following texts:
6.110 If, before he has eaten, a person's upper abdomen (epigastrium) gnaws at him, he continually has internal fever, and, when he belches, he vomits bile, that person is sick with pašittu (or) tuganu, to cure him...
6.112 As for bile that the king my lord wrote me about, saying "It came up." It is pašittu. The thick sputum came up; the gall settled down below (see above). This is not a good sign that he has been sending (the food) straight through (both) upward (and) downward. (However), he produced sweat for (only) two days. 602
That is good.
There are other texts which mention this as well, including cures.
Note that the word "bile" here is martu.
As for the demon, <PERSON> in his Melothesia in Babylonia (De Gruyter, 2014) notes that Lamaštu was considered the daughter of <PERSON>:
On the one hand martu, together with pašittu, can mean 'gall', as in the medical commentary GCCI 2 406:4... On the other hand, mārtu 'daughter' is a frequent epithet of pašittu, as in STT 138: 11' (dupl. of BAM 338 10'), la-[maš]-tu maš-tu pa-šiš-tu, 'Lamaštu daughter (of) Pašittu'. SBTU I 43, in lines 10-11, provides a different interpretation, treating Lamaštu (disease as well as demon) a parallel to another demonic disease, 'Pašittu-daughter'.
Lamaštu itself seems to be a parallel disease:
The pattern of 'ditto' notations in ll. 8-11 show that toothworm, girgiššu, lamaštu and pašittu diseases are all associated with the throat, mouth, and teeth, while remaining ailments in this group (ll. 12-18) belong only to the throat.
I haven't seen it argued, but I think it's reasonable to suppose the linguistic similarities of martu and mārtu as well as the similarities of the diseases lamaštu and pašittu were conflated and led to the association of Lamaštu and Pašittu the demons. 321