She's not going to get the message, so respond to her hysteria with composure.
Politely recite diabetes statistics at her. Something different each time. Tell her how many people die from hypos each year, how many % of people with T1D avoid exercise because of hypos (about 50%), how much T1D increases your risk of depression, etc. etc. Just say something short and then move on.
This means you're not ignoring her, yet refusing to give her the reaction she wants. And it's hard to argue with facts.