Today I'm going to sleep at 10 o'clock. Today I'm going to sleep at 10 o'clock.

You'd say this if it's nearly 10 o'clock and you're just about to go to sleep, but if you mean that it's maybe an hour before 10 and you're planning on going to sleep then you'd say "I will go to sleep at 10 o'clock"

Today I go to bedI'm going to sleep now. I'm going to sleep now.

Not sure what you were trying to say here, so guessing

Today II'm going to go to bed sleep. I'm going to go to sleep.

I'm assuming here that when you wrote this you were just about to go to bed

I am've been very tired today. I've been very tired today.

"I've been" better specifies that you were tired throughout the whole day, if that's what you mean

My eyelid iss are very heavy now. My eyelids are very heavy now.

My eyelid iss are very heavy now. My eyelids are very heavy now.

I don't have any energy. I don't have any energy.

I don't have any energy. I don't have any energy.