Is it common to experience wrist pain when you start the Double Bass?!

*in the left hand*

i would warrant wrist tightness as you adjust to the rigors of playing the DB but sharp pain may be a warning sign

Can be all sorts of aches and pains, but you won't
know what are normal and what are symptoms of
doing things 'wrong'.

Get a teacher, as experienced a professional as you
can find, then they can be in the room with you, and
that is the only way to answer your question.

Good hunting,