Absolutely not, unless bloodwork shows that you have specific deficits in those areas.
Thyroid problems are more statistically likely to occur starting in middle age, like many medical issues. But it doesn't mean there is any medical link between perimenopause and thyroid imbalances. Testosterone is not a typical medication that is prescribed for perimenopause either.
Your friend is dangerously ignorant about her own health, it's actually scary that she understands so little.