One of my three cats gulps food and now feels sick, wants to vomit but can’t, belly heaving for two days, no eating, no energy

From your description the cat may have digestive discomfort and dry heaving, but the exact cause needs vet X-rays and blood tests. Competitive gulping can cause indigestion; if the cat’s spirit and appetite are still normal, consider fasting from food and water for a day, then add active probiotics and small frequent meals.

If dry heaving and low spirit/appetite persist, it may be pancreatitis, gastroenteritis, or hairball disease; take the cat to a vet for fluids and symptomatic treatment.