Chazal prohibited measuring on Shabbat. This prohibition is mentioned in the gemara in Massechet Beitza[1] in the context of using utensils with measuring markings to transfer the exact amount of produce desired from one person to another. It also comes up in Massechet Shabbat[2] in the context of measuring a mikveh and other accumulations of water.
There seem to be two approaches to the underlying reason behind the prohibition, and they are likely to be complementary rather than contradictory. The Rambam[3] connects the prohibition against measuring to the Rabbinic prohibitions related to commerce, which themselves were enacted lest one come to write.[4] However, the Rambam[5] also mentions the prohibition of measuring among actions that are forbidden due to being connected to weekday activities and/or concerns (uvdin d’chol). The need for a second element of the prohibition is logical, as many of the applications discussed are completely unrelated to commerce. Likewise, the Mishna Berura, in discussing the prohibition of measuring, in one context invokes the reason of commerce,[6] but in another context views it as uvdin d’chol,[7] and in yet a third place mentions both reasons for the prohibition.[8]
The Beit Yosef[9] cites the Maharil, who was uncertain whether an hourglass is muktzeh because of its use for measuring time. After all, use of an hourglass is not classical measuring, which is when one uses an instrument to measure an object. Here, one uses an instrument to determine the passage of the non-physical entity of time. Whereas the Shulchan Aruch[10] leaves the matter as a doubt, the Rama,[11] like the Maharil, writes that the minhag is to prohibit even moving an hourglass, because its main usage is forbidden on Shabbat. Contemporary poskim similarly forbid use of an hourglass.[12] (Poskim agree that it is permitted to use a wristwatch.[13] A watch is better than an hourglass because a watch tells you what time it is at the moment you look at it, whereas an hourglass measures the “distance” in time between point A and point B.)
Thus, the ruling you received was indeed due to your special need, although the required need does not have to be on the same level as that which is required to permit eating on Yom Kippur. The idea that measuring is permitted in certain cases of need is explicit in the gemara,[14] which permits measuring a mikveh on Shabbat to see if it is still valid, because this measuring is done for the purpose of a mitzva. Rishonim extend the leniency from mitzva use to the needs of a sick person. The Tur[15] cites a discussion of an ancient “alternative medicine” procedure for one with a headache, which included measuring a certain distance and then saying an incantation. He cites the Maharam MeiRotenburg as permitting this because healing a sick person is a mitzva. The Shulchan Aruch[16] accepts this opinion. It is clear from the context of the above discussions that the needs of a sick person in this regard include even one who is not dangerously ill.[17] Tosafot[18] explains that we are more lenient regarding measuring for a mitzva than we are regarding most Rabbinic prohibitions, regarding which a mitzva is insufficient to permit the violation,[19] because measuring is forbidden only due to uvdin d’chol.
In your case, there are two ways of looking at how using the hourglass is a mitzva. One is that the permission you received to eat a fair amount was predicated on your ability to determine that you would not eat too much too quickly. Thus, the measuring in this case allows a weak person to eat to maintain her health. The other way to look at it is that given that you were allowed to eat, the hourglass helped you fulfill the mitzva of lessening the necessary violation of eating on Yom Kippur.[20] Either way, using the hourglass was permitted for you, even though under ordinary circumstances, it is forbidden to mark the passage of time with an hourglass on Yom Kippur.