There is not a single correct answer to this question. But before you decide whether to keep your cat, you must make sure that it is your cat causing the allergic reaction. You don’t want to go through the stress and upset of rehoming a much-loved pet if your allergic reaction is caused by dust mites.
You have to decide whether the severity of your allergic reaction means you need to re-home your cat.
In some cases, the symptom-easing tips included above are enough to make living with a cat sustainable, but other people find that their allergic reaction makes living with a cat unbearable.