Hi, welcome to the ehealth forum and I am glad to help you.
You seem concerned by the nausea for 1 month with the finding of small gallstones and sludge in gallbladder on ultrasound.
Many illnesses associated with the intra-abdominal organs have symptoms of nausea and vomiting. These include digestive organ diseases, for example: hepatitis, gall bladder disease etc.
So, it is quite possible that your symptoms might be due to gallbladder disease but you must consult your personal physician for definitive diagnosis and to rule out other causes of nausea as the same is not possible online.
Hope this helps. Take care.
Note: This answer is not intended as and does not substitute for medical advice - the information presented is for patient education only. Please see your personal physician for further evaluation of your individual case.