The same thing happened to me around a month in (and also my eye lids felt very dry even though I don't put the BP anywhere near them). I just kept putting lotion on my neck whenever I could throughout the day and now it's fine (but I still add lotion to my neck morning & night). I did use a little Elizabeth Arden Eight Hour Cream on the very dry spots but it's kind of expensive; I'm sure there are more affordable options out there.Eyelids still feel a little dry but they're improving and face looks good so...
Good luck!
It really depends on your skin when it can fully adjust. For me it took months for my skin to feel like skin again. No dryness, no itching, no redness, no flakes...it took maybe around 4 months. So gauge the skin on your neck, maybe it needs more moisturizer, maybe add some jojoba oil, maybe switching to a moisturizer that suits your skin/climate more is also a good thing.