Normal blood tests but period came a month late? worried it could've caused a hormonal disturbance and cause hair loss.

Unlikely: Menstrual disturbances are usually caused by a hormone problem. However, an isolated delayed menses would not likely cause hair loss. I suggest that you work with your gyn or pcp to try and learn what might have been the problem. Occasional delayed menses can be very difficult to understand, but if the problem recurs then more likely to get an answer. Best wishes.