Hello, if this often occurs you could have Lagophthalmos, which means the inability to completely close one's eyes when sleeping or resting.You can use saran wrap or wear goggles at night to trap moisture so that their corneal surfaces do not dry out while they sleep. You can also use preservative-free drops. You can still suffer an allergy to dust mites and down feathers.
There are lots of reasons can make your eyes appear red when you lay down.
You may have internal thermal, or some inflammations, cervical spondylosis, etc.
Internal thermal and inflammation can be easily solved by yourself. You can drink some honey diluted with water. Use some artificial tears. Eat less peppers, more fruits and vegetables. However, for your own sake, you'd better see a doctor, then accept a check-up.