I lost half of my hair in a 2 month period.Is it a emergency?

Without photos or more history, this is a difficult case to comment on specifically.  In general, pattern baldness can seem rapid since we generally lose about 50% of our hair before we recognize a visible change.  Once the change is noticed, then it seems the hair loss is progressing more rapidly but really it has been at a steady state.  However, there are several medical forms of hair loss that can be accentuated by stress and can be rapid in onset.  Alopecia Areata is the condition that first comes to mind.  You should seek medical care from a hair loss physician right away. 

Without knowing all your history from A to Z, and seeing your scalp up close, it's not possible to assess the cause of your hair loss.Please see a dermatologist for full evaluation if you are worried.Are there situations where skin rashes and hair loss are associated with more concerning, emergent situations? Yes, but that would be quite rare. It is not possible to offer any assessment of your situation with the info given.

You need to see a good doctor to determine what is happening to you. Without more information, it is impossible to determine what is happening and what is causing it.