The other key factor your not taking into consideration, is the egg needs high & constatnt humidity. It is not going to get that with you carrying it around. As someone else posted, you will not be able to put this chick IF it hatches with your other chickens. You will have to keep it in the hose under a heat lamp for 4-6 weeks or longer depending on where you live, until it is fully feathered. It will be all alone that whole time. It really is not fair to the chick to hatch it by itself. Another thing to consider is that if the chick does not grow, and it is warm, the egg could go rotten and rotten eggs explode. Do you really want to take the risk of a rotten egg exploding under your clothes/armpit, etc.? You really need to wait until you have a proper incubator, there are great instructions on here to make homemade ones, and you need to put in a few eggs at least, so that if they do hatch, they will have hatchmates to be with.
One last thing, as a mother, I would be so upset with my daughter "hiding" this from me. Just think about it.