Hmmmmm scratching my head a bit and may ramble...
Went through this same thing with our soy introduction - sudden screaming NWs and constipation, both were problems he had when he went form milk formula to soy formula. I think I posted here asking for advice so will try to find that thread for you and link it.
One thing I would do first is a routine check and brainstorm ANY other reasons you can think of for NWs? Is he sleeping well in the day? Separation anxiety? Canines coming in, other tooth shifting perhaps occuring? I found that after the front teeth it's been difficult to get a good look in DS's mouth to see the next ones coming in as he just does not want me looking. But, it would not be strange for him to be continuously teething at this stage - to cut some and then have more moving up and sitting at the surface very shortly after. And, although my DS cut his first teeth quickly and painlessly, the more he teeths (the larger the teeth are) the more pain he is in, and the longer they are taking. Are topical gels and/or pain meds having any effect?
Poop - I would be concerned with the constipation as my paed always told me that constipation was more worrisome than diarrhea. But, when you say constipated, do you mean he is really straining to go, and/or not going regularly enough? Or is his stool just more "formed" than it used to be? As they get on more solids and more grains, poop starts to look a bit more "adult like" and is not as soft and smushy as baby poop was. Can you identify any other cause of constipation - not enough fruit or fibre, any other changes in things, etc?
I know how hard it is to go back on milk after you've started - once we started milk I was determined that DS was going to have to be VERY sick for me to consider dairy-free again. Fortunately, we didn't have any major problems - a massive run of diarrhea and a week or so of NWs and lots of screaming, which I was able to confirm was teething. And I'm pretty sure we did it by just sticking with things, mainly out of my stubbornness.
I think that with stopping the milk, you may not see an immediate change, IF that is the problem. It will take a while (few days to few weeks?) to get the milk out of his system, and so it may or may not be clear if that was the issue or not. Just at thought.
How old is he now - I can't see the date on your OP to do the math, but I think I remember your OP was not that long ago..so he is nearing a year now? Generally docs do like to do a milk challenge at about 12 months or so - are you getting any support in this from a GP/paed/dietician, aside from your HV? HVs tend not to be really clued up on this in my experience (assuming you are in UK). We had a hospital paed who saw us when DS was diagnosed MSPI and a hospital dietician as well. In my area, all babies were sent to hospital for a milk challenge with the dietician at 12 months, where they were given bits of milk over the course of the day to watch for reactions. (We moved abroad before we were able to do this so I can't provide more detail than that...other than that here in Germany they do it as well, but I had done my own milk challenge before speaking to our new paed here about it). So, you should be able to at least get your GP to refer you to someone who will do a milk challenge for you and might give you more support and advice than your HV.
Can you request allergy testing? Allergy testing is not 100% as sometimes the problem with milk is an intolerance, which won't show up on an allergy test. (Allergy is an immune system reaction, intolerance is a bowel reaction, most doctors won't bother differentiating between the two as the point is that dairy free is still the only option). So, as much as allergy testing may not be 100%, if you get a postive, then it's accurate. If you get a negative then....well, there's a good chance it is negative but not 100%. I'm not sure if milk allergy tests can be done by scratch or hair testing in your area, here in Germany my own paed can not offer that way of testing, she is only able to do blood tests.
I spose that's all, really, and don't think I have been of much help. I suppose my last final thought is that if he is older than one, I would give it another week or so on the milk and see if you can lose the NWs or find another reason for them. If the constipation is quite bad, then I would go off of the milk and see if it improves.
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Sorry if I am not helpful, just trying to think out loud for you!
mashi