It's not up to me to decide if the Lord wanted to tell you something specific with the no. 24. What I do know is this: We find the number three times very closely connected in the prophets of Haggai and Zechariah. Both prophets acted during the latter part of the Babylonian captivity and I'm reminded about these three prophecies when reading the number 24.
Haggai 2:11, Haggai 2:21 and Zech. 1:7.
Look at the dates of the prophecies: in the second year of Darius, on 9/24 (Haggai twice) and 11/24. Zech. 1:12 also tells us that the Lord had been angry with the land of Judah for 70 years. Zechariah then prophecies about the events of the Last Days.
24 = 8+8+8, may illustrate new beginning. We know that Daniel's 70 week-years are almost over and a new dawn and new age (the Millennium) is near; the Revelation of Christ and the Day of the Lord are at hand!
May the Lord provide His mighty presence and consolation to your sister Christine, yourself and loved ones during these terrible and tempting days of her illness.