These dark, velvety patches under your arms and across your chest and back are commonly called acanthosis nigricans. Together with your periods being delayed for three months, this usually points to insulin resistance or PCOS rather than a skin problem on its own.
Next Steps
A urine
pregnancy test is also worth doing to rule out pregnancy, miscarriage or an ectopic pregnancy as reasons for the delayed cycle, alongside a fasting insulin, glucose and hormone panel and a pelvic ultrasound. Treating the underlying cause usually fades these patches over time.
Health Tips
Please see a gynaecologist or endocrinologist in person for this, since photos alone can't rule out a separate skin condition causing the darkening.