Dr. Conrad Murray -- Allow Me to Introduce Myself ...

Of all the things you DO NOT want to hear after fainting aboard an airplane, "I was Michael Jackson's doctor" has to top the list. But that's exactly what happened to a woman this morning.

As TMZ first reported, Dr. Conrad Murray came to the aid of a woman on board a flight from Houston to Phoenix after she passed out.

TMZ spoke with the woman, who tells us she got lightheaded on the flight and "fainted for like 30 minutes." She says when she regained consciousness, she had an IV in her arm and Murray was standing over her. She says he told her, "You probably know me ... I was Michael Jackson's doctor."

She's a little fuzzy on the details after that, but one thing she is certain of -- she is incredibly grateful to Dr. Murray.

When asked what she would say to Dr. Murray, she told us, "Thank you so, so, so much. Thank you for all your help. Thank you for helping me even without knowing me. Thank you."