I'm usually very sleepy recently.

Since last June I've usually been getting up at 5 am to study English.

大変だな！
D:

I think that I'll get used to getting up so early, but I probably won't.

I think it's better to write:
"I thought that I'd get used to getting up so early but I haven't at all."
since it's information from last June.

When I join the meeting at office, I feel really sleepy.

Of course I mustn't fall asleep.

I have to just work there!

頑張ろう～

I'm husuavelly been very sleepy recently.

You use "have been" when you have been doing something and (for most of the time) still are.

I husuavelly been getting up at around 5 am sincefrom last June sto I could study Egnlish.

I thopeing that I'll get used to getting up early in the morning, but I dwon't think I will.

BecauseIf I'm can getting up at 5 am, I'm very sleepy.

When I joined the meeting at workffice, I was feeli strong very sleepy.

Of course I must'nt( I'm not quite sure how to spell this, but i would write "must not" ) fall asleep.

I have to just started working there!