Prayer of one who has some impurity on his person
Question

                I am a military student in one of the military academies, and I have to stay there five days a week. My problem is that, because we have little time, I have to do wudoo’ and pray within a short period of time, then go back to training. The problem is that when I go to the bathroom to relieve myself and take a shower, some drops of urine continue to come out a short while later. I keep some handkerchief to wipe whatever is left of the drops, so that my underwear will not become impure, and so that I can do wudoo and complete the prayer. But my question is that I still keep the handkerchief with which I wiped the urine in my pocket. I am confused about the fact that I'm still carrying the impurity with it. How can I go and pray with this unclean handkerchief in my pocket? Please note that I cannot throw it away, and get a new handkerchief every time I go to do wudoo and pray. I hope that you can give me a solution, because I find it difficult to go to the bathroom, and then wait a while for the drops to come out, and then go again to wipe away the drops. Then I think: is it permissible for me to pray with this handkerchief in my pocket? Please note that I am absolutely certain that the drops of urine come out a short while after going to the bathroom.
Praise be to Allah.Firstly: 
If the matter is as you 
    describe, that a few drops of urine come out shortly after urinating, and 
    you put a piece of cloth to prevent your body and clothing becoming 
    contaminated, then when you want to do wudoo’ you have to remove the cloth 
    and clean yourself, and wash the site where the urine has come out, or clean 
    yourself with the handkerchief by wiping your private part,  and it is 
    essential that you wipe it no less than three times, because of the report 
    narrated by Muslim (262) from Salmaan al-Farisi (may Allaah be pleased with 
    him) who said: The Prophet (blessings and peace of Allah be upon him) 
    forbade us to clean ourselves with less than three stones. 
Secondly: 
It is not permissible for 
    the person who prays to carry any impurity during the prayer, and his prayer 
    is not valid if he does so, according to the majority of scholars. See: 
    al-Mughni (1/403) and al-Majmoo’ (3/157). 
Based on that, if you carry 
    the handkerchief in your pocket, your prayer is not valid. You should take 
    out that handkerchief and place it beside you, or in your shoe that you have 
    taken off, or you should keep with you a bag in which you may place the used 
    handkerchief. If it so happened that you forgot the handkerchief in your 
    pocket and you finished your prayer, then you do not have to do anything and 
    your prayer is valid. If you remember it during the prayer, then you could 
    take it out from your pocket and place it beside you, and be careful not to 
    annoy anyone else with it. 
It says in Nihaayat 
    al-Muhtaaj: If it is the matter of a choice between throwing the 
    impurity away now so that your prayer will be valid, but that requires 
    throwing it in the mosque because you are there, or not throwing it away so 
    as to protect the mosque from impurities but that will invalidate the 
    prayer, then what I think is more appropriate is to pay attention to the 
    validity of the prayer, and to throw the impurity away now in the mosque, 
    then remove it immediately after finishing the prayer, because by doing that 
    you can combine validity of the prayer with keeping the mosque clean. But it 
    is acceptable to throw away the impurity and delay removing it until you 
    have finished the prayer, because of the situation. End quote.  
We do not think that 
    keeping enough handkerchiefs to suffice you during the time you have to stay 
    in the camp is something that will be too difficult for you, if you work out 
    how many of them you need. 
And Allah knows best.