My symptoms (probably of GBS not CIDP) started in a similar way–with pain in my left arm. It actually was mainly left arm above the elbow and then in left shoulder and then neck and back of head. After this had been going on for several months, I got the hand and feet tingling and numbness. The hypothesis was that the pain in the shoulder and neck was from weakness in holding my head/body and made worse by carrying pretty heavy bags of papers and books (mainly on left side). The pain in my shoulder and neck DID go away rapidly after a trigger point injection and stopping carrying anything heavy. The rest of this stuff is still with me (better, but still with me). The time course of onset is odd for GBS and for CIDP really, but there has not been definite progression in three years and I am better.
I would guess that you carry your child around and maybe other times have tug on the neck. Try to not carry anything heavy for a few days and see if the neck is better.
I had two spinal taps and they were no big deal. You just need to curl up really well and make sure that the person doing it knows what they are doing. You can ask for medication to help you relax if this might help you.
The spinal tap and EMG are the best ways to diagnosis CIDP. A nerve biopsy is sometimes done, but lots of places do not recommend this unless the other tests do not confirm the diagnosis.
Treatment for CIDP does not need to affect fertility and most do not.
There is another neurologic process called DeVics or neuromyelitis optica that they thought about in me because of the neck pain (and because of an oddity on the neck MRI). this is a central nervous system process and more similar to MS than to CIDP. One can see changes on MRI of the spine. A blood test can help to confirm it because of a specific antibody. It is rare and also it would be unusual for pain to be mainly one sided as it is for you and it would be unusual to have a peripheral neuropathy like distribution of numbness (below elbows and knees). One would expect more likely numbness below the level of the problem in the spinal cord. I do not say this to add to worry, just to emphasize that the MRI and spinal tap are important. It sounds like your neurologist is proceeding in an appropriate manner in looking at all of this.
It is scarey. Take each day at a time and try to not get overwhelmed by worry. There are a lot of variations in severity and manifestations. Lots and lots of people have milder forms.
WithHope for a cure of these diseases