First, I am sorry that you are struggling, and that things are rough.
In answer to your question, my answer is 'yes, I am okay'. I give that answer not based on society's expectations, but my own. I have struggles and challenges on a daily basis, but none of them are more than I can handle. For that, I am grateful. That may change today, tomorrow, or next week, but for now, yes, I am okay.
"Are you okay?" is a question that is asked for many different reasons, and some are more sympathetic and empathetic than others. It can convey impatience, certainly, but it can also be an offer to help. That help might be as simple as offering an ear, letting the other person know that the asker cares and stands ready to do something, however small, to improve things if help is wanted, needed, or allowed. It is an invitation to open walls, to let down barriers, or to communicate that space is what is needed.
So while answering simply to dismiss the question, or to turn it aside, is perfectly fine, please keep in mind that some are asking because they would like to help.
At what point do we become 'not okay' is subjective. How much can we stand on our own? How much do we want to stand, how much do we want to accept? Can we still do this on our own, or do we need help? Ultimately, I think that each of us needs to answer that question for ourselves, and if the answer is 'yes', then keep plugging on. If it is 'no', or when it becomes 'no' then we need to look inside and figure out what kind of changes we can make to the situation -- either alone, or with help ... of family, friends, professionals, and sometimes even a stranger whose only qualification is being in the right place at the right time and who takes a moment to care.
I hope that things get better, and that you will find something or someone to help you recharge so you no longer feel so drained. There are good things out there, even if they sometimes are very hard to find.