Is this a symptom of the immunosuppressants?

3D structural formulae of Azathioprine

Okay, so I think the immunosuppressants may be working now. I have been hopeful for just over a week, but dread horror I THINK MY HAIR IS FALLING OUT! So here we are again - a balancing act? a fine line?  I'm not sure what to call it but it often seems to come to this - a pay out for improvement.  Am I prepared to lose my "crowning glory" to improve? The answer would be clear if the improvement was more obvious but so far I have only noticed 1 symptom has gone, amongst a myriad of symptoms. I know I will keep taking the Imuran for now but not sure how long.
I just checked MedicineNet for the listed side effects of Azathioprine, the drug I am on:
"SIDE EFFECTS: The most common serious side effects of azathioprine involve the cells of the blood and gastrointestinal system. Azathioprine can cause serious lowering of the white blood cell count, resulting in an increased risk of infections. This effect is reversed when the dose of azathioprine is reduced or temporarily discontinued. Azathioprine can cause nausea, vomiting, and loss of appetite, which may resolve when the daily dose is reduced or divided and taken more than once a day. Azathioprine can cause liver toxicity (for example, in less than 1% of rheumatoid arthritis patients). All patients taking azathioprine require regular testing of blood for blood cell counts and liver tests to monitor for side effects of azathioprine. Other side effects encountered less frequently include fatigue, hair loss, joint pains, and diarrhea."
I was hoping not to find it listed as aside effect. I was hoping I was imagining it.