Appendicitis: This is the most likely diagnosis given the classic presentation of worsening abdominal pain in the right lower quadrant, often accompanied by vomiting. The pain typically starts around the navel and then moves to the right lower abdomen.

Gastroenteritis: Inflammation of the stomach and intestines, usually due to infection, can cause vomiting and abdominal pain. The pain can be diffuse or localized and may not always fit the classic appendicitis pattern.
Intestinal Obstruction: A blockage in the intestines can cause severe abdominal pain, vomiting, and constipation. The pain can be generalized or localized, depending on the site of obstruction.
Mesenteric Lymphadenitis: Inflammation of the lymph nodes in the mesentery (the tissue that attaches the intestines to the back of the abdominal wall) can mimic appendicitis, with pain in the right lower quadrant and vomiting.

Ectopic Pregnancy: Although less common, an ectopic pregnancy can present with abdominal pain and vomiting. It's crucial to consider this in women of childbearing age, as missing this diagnosis can be fatal.
Perforated Visculitis or Ulcer: A perforation in the stomach or intestines can lead to severe abdominal pain, vomiting, and potentially life-threatening peritonitis.
Ovarian Torsion: Twisting of an ovary can cause sudden, severe abdominal pain, often accompanied by vomiting. This is a surgical emergency.

Meckel's Diverticulitis: Inflammation of a Meckel's diverticulum, a congenital anomaly of the small intestine, can cause abdominal pain and vomiting, similar to appendicitis.
Intussusception: A condition where a part of the intestine slides into an adjacent part, potentially causing bowel obstruction. It's more common in children but can occur in adults.
Inflammatory Bowel Disease (IBD) Flare: Conditions like Crohn's disease or ulcerative colitis can cause abdominal pain and vomiting during a flare-up. While not typically new onset, a first presentation could be mistaken for other acute conditions.