Cyclic Vomiting Syndrome (CVS): This condition is characterized by recurrent, severe episodes of vomiting that are separated by periods of normal health. The cyclic pattern described, with symptom-free periods followed by weeks of nightly symptoms, aligns closely with CVS. The improvement after vomiting and the lack of abdominal pain or cramps also support this diagnosis.

Gastroparesis: Although typically associated with abdominal pain and bloating, some cases of gastroparesis can present with nausea and vomiting without these symptoms. The cyclic nature and improvement after vomiting could fit, but the absence of other symptoms like bloating or early satiety makes it less likely.
Functional Nausea and Vomiting: This diagnosis could be considered given the chronic nature of the symptoms and the lack of identifiable triggers or organic causes. However, the cyclic pattern is less typical for functional disorders.
Rumination Syndrome: Characterized by the effortless regurgitation of food, which may be re-chewed, re-swallowed, or spat out. While it doesn't perfectly match the described symptoms, some elements like feeling better after vomiting could be interpreted as related.

Gastrointestinal Obstruction or Partial Obstruction: Although less likely given the cyclic nature and lack of abdominal pain, intermittent obstruction could potentially cause such a pattern. It's crucial to rule out this possibility due to its potential severity.
Inflammatory Bowel Disease (IBD): Conditions like Crohn's disease or ulcerative colitis can present with a wide range of gastrointestinal symptoms, including nausea and vomiting. The absence of other typical symptoms like diarrhea or abdominal pain doesn't rule out IBD entirely.
Neurological Disorders (e.g., Brain Tumors, Chiari Malformation): Rarely, neurological conditions can cause cyclic vomiting. Given the potential severity of these conditions, they must be considered, even if the presentation seems atypical.

Mitochondrial Neurogastrointestinal Encephalomyopathy (MNGIE): A rare genetic disorder that affects the digestive system and nervous system, causing symptoms that can include severe vomiting.
Eosinophilic Gastroenteritis: A condition characterized by eosinophilic infiltration of the gastrointestinal tract, which can cause a variety of symptoms including nausea, vomiting, and abdominal pain.
Other Metabolic or Genetic Disorders: Various rare metabolic or genetic conditions can cause chronic or cyclic vomiting. These would be considered if common causes are ruled out and there are other suggestive symptoms or findings.