I am sorry to hear of your misery!! That sounds awful! While many with MS have nerve pain to some extent, it does appear to be rare to have pain to the extent you are. You need a pain management doctor!
There are pain meds out there that can help. I am not experienced with all the different pain meds. I do have some nerve pain but I generally can treat it with ibuprofen! I am sure that wouldn't touch what you are experiencing.
You may want to post on the chronic pain board here. There are members with a ton of experience there. We have lots of members that post on more than one board so don't feel like I am encouraging you to leave. I just want you to have some good feedback, and I am worried you won't get much here. Your experiences are not typical.
Please keep us posted and ask any questions you may have. It seems you are questioning your diagnosis a bit. Have you considered a second opinion? What your neuro said about the adverse reaction to an anti-depressant sounds plausible. Are you seeing an MS specialist? Something to consider. Your local chapter of the MS society will have a list of MS specalists nearest to you. Best of luck!! I can't imagine pain while caring for a baby.