Step 1: Identify the key clinical features.
The patient is a teenage girl with: (1) transverse vaginal septum -- an obstructive Mullerian anomaly; (2) dysmenorrhoea -- painful periods; (3) chronic pelvic pain (CPP).
Step 2: Link obstructive anomaly to endometriosis.
An outflow obstruction (transverse vaginal septum) causes retrograde menstruation, where menstrual blood and endometrial cells flow backward through the fallopian tubes into the pelvic cavity. These ectopic endometrial cells implant on peritoneal surfaces and behave under hormonal influence, causing cyclic inflammation, scarring, and chronic pelvic pain -- the hallmarks of endometriosis.
Step 3: Consider secondary dysmenorrhoea in adolescents.
Secondary dysmenorrhoea typically appears 12 months post-menarche and is associated with progressively worsening pain, CPP, mid-cycle or acyclic pain, and irregular or heavy menstrual bleeding. Common etiologies include endometriosis, adenomyosis, and obstructive anomalies.
Step 4: Exclude the distractors.
Tubo-ovarian abscess requires pelvic inflammatory disease context. Dermoid cyst and theca lutein cyst do not explain the combination of obstructive anomaly with dysmenorrhoea and CPP.
Conclusion: The correct answer is Endometriosis.