Can one become suddenly ambidextrous?
Normally in a right handed person the left hemisphere is considered dominant.  However, a new lesion in the left hemisphere can cause loss of this dominance so it is possible that this has occurred.

Alternatively, if the subject is now able to write using both hands concurrently but different material, it suggests that the two hemispheres are disconnected, the so called split brain syndrome which occurs with lesions of the corpus callosum.  However, ambidexterity is not described in that syndrome.

Anyway, you need to consult your physician.