The most moral and non-offensive term would be a “Resident of (Name of home or place)”, resident in a personal care home(or some other term for a care home), and sometimes a Patient- but only if the patient is living in a medical care home, like part of a hospital for example. Awkwardly explained, but I hope you understand!
The person is exhibiting signs of an allergic reaction. Asking questions such as "how long has this been happening" simply extends the time the person is suffering. However, asking if they have an epi pen can solve the issue immediately.