Is it normal to feel your heartbeat when lying down?

See a doctor immediately! No, I would not think this is normal. The key here is the pain you feel in your chest.

Awareness of your heartbeat can be a simple(ish) sign of anxiety, or can be due to cardiac causes which are mostly benign. The pain in your chest may also be due to the effects of anxiety, but any chest pain needs to be checked out.

I am a cardiac patient so I know the need to respect the heart and look after it...