Hi there,

In all honesty, many natives would use either without thinking much about it.

However, if we do want to try to find a difference, I would say this:

I'm feeling sleepy 💤 - makes you mentally locate the action slightly further back in time

( something you are perhaps aware of already)

I feel sleepy 💤 - makes the idea more immediate for the speaker amd listener.

Definitely though, 'I feel sleepy' is better and more common to use!

I think I am also feeling sleepy is better than I also feel sleepy because it sounds more appropriate grammatically. By the way both mean the same thing.

which is better to use?

They mean the same thing