From the history available, a possibility is that the needle hit a nerve in the cubital fossa since there are many closely placed structures in that area of the body. The sensation you describe is that of a nerve injury
along the distribution of the nerve on the forearm. Nerve injuries during injections or intravenous lines are quite common. This could have happened because you might have not kept your hand still during the procedure. Nerve injuries can take long to recover depending on the extent of injury. If it is a first degree or small injury it may take from few days to few months to recover.
It is advisable you visit your doctor if the pain is excrutiating or lasts longer.
Hope this helps,
Dr A Rao