No, it is not "normal".
The double vision is due to a palsy of one or more of the cranial nerves. The specific cranial nerves can be identified by the type of double vision. The 3rd and 12th cranial nerves are commonly affected.
It can be due to a tumor, infection or injury. It can also be due to diabic neuropathy.
In any case, you require an evaluation by an opthamological neuorologist.
Depending on the etiology, it may come and go. In a worse case you will end up with one eyeball "frozen" in position, so it's best to get a professional evaluation.
At the very minimum you require an MRI, an MRA and a diabetic screen to include an hba1c and either a fasting glucose test or an insulin clamp protocol.
Did they indicate you might need lumbar puncture again to decrease spinal Fluid? Are you taking meds for This?