Help with cold

My month old has sadly got a cold off her older sister, she’s refusing to sleep in her cot and only wants to lay/sleep on me. Just now I put her down and she started choking because she’s always congested whenever she’s laying down. I’m very nervous to sleep now as I don’t her choking while I’m sleeping. Does anyone know what I can do to help her with this cold??? I know she’s still young for medicine