The bed in my bedroom can only have its head in the west and its tail in the east. Is this appropriate?

No problem, as long as your bedside has a backer, that is to say, the bedside is against the wall, or the headboard is higher than your head and does not leak water. When I sleep at night, I often dream that Baihui point on my head has a headache due to the wind or there is no backer by my bed. If you want to dream, try to sleep at the end of the bed.

As for the saying that I don't know when I will arrive in the eastern sky, there is indeed a saying in Feng Shui that the orientation of the bedside is placed according to the life, but as long as the placement method is correct, the orientation problem is not the main problem.