An epipen was administered and an ambulance rushed her to hospital where she was stabilised by ICU doctors who gave her strong doses of adrenaline to reduce the swelling in her throat.
"I'm still very unwell but I'm past my anaphylactic reaction - I'm very lucky that I did get through it," she said, adding it was one of her worst reactions to date.
The incident prompted calls from allergy support organisations asking Aldi to scrap the 'Dairy Fine' labelling.
"CEO of Allergy and Anaphylaxis Australia Maria Said told 7NEWS.com.au the issue is a "life or death" one."
"If they [Aldi] do keep the Dairy Fine brand, it's got to be in a clear, bold font legible on foil and cellophane.
"They don't want to wait for a fatality to finally make a change," she said.
Kaley revealed she intends to bring the episode to Aldi's attention once she is well enough.
"I'll definitely be taking it further. Their packaging is very misleading and not clear."
An Aldi spokeswoman said it was unable to comment as the issue has not been reported to them.
If brought to their attention, she said it would file a report to the Australian Food Safety Authority for review.
This story originally appeared on 7NEWS.com.au
