Where to put an adjective to avoid ambiguity?

The essence of this question is not about style. It is foremost about avoiding ambiguity.

The sentence is "She called me." If I want to use the word "sniffling" to describe the caller, where should I put it? I don't want to use the adverb "snifflingly".

If a noun is used instead of the pronoun 'She', it's very clear to say "a sniffling child called me".

I would say:

She called me, sniffling.

That would be an example of an absolute adjective:

Absolute adjectives do not belong to a larger construction (aside from a larger adjective phrase), and typically modify either the subject of a sentence or whatever noun or pronoun they are closest to; for example, happy is an absolute adjective in "The boy, happy with his lollipop, did not look where he was going."

If you must use the word "She", I would put the adjective at the end of the sentence:

She called me, sniffling.

Note that without proper punctuation this may be ambiguously interpreted, with an alternate interpretation suggesting that "sniffling" were a name:

She called me "sniffling".