I assume you mean physical 3D illness and not separation sickness?
I’ve seen it called empathic resonance… you’re so attuned to each other’s energetic vibrations that when one twin experiences physical discomfort, the other absorbs and mirrors those imbalances.
I’ll get random bouts of something - a headache, fatigue, weird aches - and sure enough, when I check in with someone who still talks to him, he’s going through the same thing. Same symptoms and same time. The energetic cord doesn’t care about no contact. From what I understand, twin flames share an energy bond that stays active regardless of physical distance or how much you try to disconnect. That cord shares information and energy constantly. Even runners who have no clue what’s happening still receive through it.
I’ve accepted it, just as it is. Before I left, we’d both get the same random cold, the same fatigue hitting us on the same day, both lose our appetites at the same time. Recovery was always parallel to.
Plus the connection itself creates physical symptoms during intense phases. Flu-like symptoms, headaches, fatigue, the body releasing old stuff as energy moves through. If you’re both processing at the same time (which you often are), you’ll both manifest it physically at the same time too.
Anyway, you’re not imagining it.