Ectopic Pregnancy: Given the patient's symptoms of missed period, lower abdominal pain, and low-grade fever, along with being sexually active and not using birth control, ectopic pregnancy is a highly plausible diagnosis. The location of the pain (lower right abdominal) could suggest a right-sided ectopic pregnancy.

Ovarian Cyst: Ovarian cysts can cause lower abdominal pain and are common in women of reproductive age. A ruptured cyst could also explain the acute onset of pain and low-grade fever.
Pelvic Inflammatory Disease (PID): PID is an infection of the female reproductive organs and can cause lower abdominal pain, fever, and nausea. The patient's sexual activity without birth control increases the risk of PID.
Appendicitis: Although the pain is described as lower right abdominal, appendicitis should be considered, especially if the pain has migrated or is severe. However, the absence of severe pain, vomiting, or changes in bowel habits makes this less likely.

Ruptured Ectopic Pregnancy: While mentioned as the single most likely diagnosis, it's crucial to emphasize that a ruptured ectopic pregnancy is a medical emergency requiring immediate intervention. Missing this diagnosis could be fatal.
Ovarian Torsion: This is a rare but serious condition where the ovary twists, cutting off its blood supply. It can cause severe abdominal pain and requires immediate surgical intervention.
Appendiceal Abscess or Perforation: If appendicitis is present and progresses to abscess or perforation, it can lead to severe consequences, including peritonitis and sepsis.

Mittelschmerz: This refers to mid-cycle pain associated with ovulation. While it could explain the lower abdominal pain, it doesn't account for the missed period or low-grade fever.
Endometriosis: Although endometriosis can cause chronic pelvic pain, it's less likely to cause acute symptoms like those described. However, it could be considered if other diagnoses are ruled out and the patient has a history suggestive of endometriosis.