From Macmillan Dictionary
2) a situation that gets worse and worse
or as a verb
2) to continuously become worse, more, or less
Usually with regards to feelings it is an established feeling becoming more pronounced. In most cases, the spiralling feeling is negative, like depression. In your case, I think it means that they (the author) felt worse because they felt they were being ignored, but that assumes that they felt bad in the first place. It might mean that they repeated the shutting out behaviour themselves but on a grander/more deliberate scale.
"Shut out" (again from Macmillan) means:
if you shut something out, you stop yourself from seeing it, hearing it, or thinking about it
So they refused to even think about the other person, let alone contact them. Alternatively, I've seen "shut out" used to describe a situation where one person hides their feelings from another yet maintains contact.
So, in simple terms, when "you" ignored me, "I" ignored "you" back, with even more ignoring.
Note: "with even more ignoring" is playful English at best - I think it gets my idea across adequately, but I wouldn't use that phrase in formal writing.