mai thak gaya(f- gayi) hoon मैं थक गया (गई) हूँ.
u will say "gayi" because u are female.
sorry-
kshama kijiye क्षमा कीजिये
maaf kijiye माफ़ कीजिये
u can also say "sorry" itself (सॉरी)
i m busy-
main vyast hoon मैं व्यस्त हूँ.
main busy hoon मैं बिज़ी हूँ.
i have been busy-
this one is difficult to translate exactly, because tense suggest that that the action happened at an unspecified time before now, and here in hindi we need to tell that so i used samay(time) to make intention clear. i think the closest we can get is
main kuchh samay se vyast hoon