If you’re over 45 the guidelines are not to do blood tests.
www.nice.org.uk/guidance/ng23/chapter/Recommendations
Your symptoms do sound like peri menopause.
1.3.2 Explain to women that as well as a change in their menstrual cycle they may experience a variety of symptoms associated with menopause, including:
vasomotor symptoms (for example, hot flushes and sweats)
musculoskeletal symptoms (for example, joint and muscle pain)
effects on mood (for example, low mood)
urogenital symptoms (for example, vaginal dryness)
sexual difficulties (for example, low sexual desire).
Reason why the guidance is not to do tests
In otherwise healthy women over 45, is that perimenopause and menopause can be diagnosed based on clinical history alone. In this age group, laboratory tests, particularly follicle-stimulating hormone (FSH), do not help with the diagnosis because hormone levels fluctuate during the perimenopause.
www.nice.org.uk/guidance/qs143/chapter/quality-statement-1-diagnosing-perimenopause-and-menopause