I am guessing that your Mombasa flight is in the morning - 7am or so.
What I do when I come in in the middle of the night like that is:
Collect my luggage from the carousel and put it on a trolley. I then go to the Customs people and ask them if I can wait in the Baggage Hall because I have a Domestic flight in the morning. They always agree! This is much safer than sitting in the Arrivals place and less draughty than waiting in Domestic. (With the current security system, I don't know at what time they will allow you into the Domestic departures).
I have not needed to do this for a couple of years now, but last time I did it, there was a row of seats to the left as you face the exit. I then sit on a seat, put my feet on a trolley and snooze!! (I push the saet against the wall first.) The staff around are usually very friendly. You may find someone who will offer you a better seat! The loos are on the other side of the Hall.
Around 2 hrs before my next flight, I greet the Customs people, exit the Baggage Hall, turn LEFT, cross the car park and the road and enter Domestic. It is about 200 yards! (It is a good idea to go if you hear a big flight arriving!!)
There is a Transit Lounge, but it is before you do passport control, so your luggage will just sit in the Baggage Hall. You can go to the Transit Desk and ask their advice. Which Airline are you using (arrival and to Mombasa)?
If you'd like to discuss this a bit more, then e-mail me on firstname.lastname@example.org
I am also a single female and usually travel alone!