Praise be to Allah.
Purifying oneself from minor impurity requires making the water reach all parts of the body that have to be washed when doing wudoo’ in the case of minor impurity, and making it reach all parts of the body when cleaning oneself in the case of major impurity (i.e., ghusl). It also requires removing anything that prevents water reaching those parts, which include the nails: if something prevents water from reaching them, such as nail polish and the like -- with no excuse -- then wudoo’ is not valid, and the same applies to ghusl.
End quote from al-Mawsoo‘ah al-Fiqhiyyah, 5/171
In Saheeh Muslim (243) it is narrated from ‘Umar ibn al-Khattaab that a man did wudoo’ and omitted a place the size of a fingernail on his foot. The Prophet (S) saw him and said: “Go back and do your wudoo’ properly,” so he went back, then he prayed..
Al-Nawawi said: In this hadeeth we see that if a person omits a small part of that which must be purified, then his purification is not valid. There is scholarly consensus on this point.
End quote from Sharh Saheeh Muslim, 3/132
If it is necessary to put something like nail polish on the nails because of some medical problem or the like, then in this case there is a concession (rukhsah) allowing it, and it should be wiped over when doing wudoo’ or ghusl. This “nail polish” comes under the same ruling as dressings that are placed on injuries or wounds.
It says in al-Mawsoo‘ah al-Fihqiyyah (15/108): With regard to the ruling on wiping over dressings: the bandage or dressing, or whatever treatment is applied to the wound that prevents water reaching it, such as oils and the like, should be wiped over. End quote.
Maalik said concerning the nail that has dropped of: There is nothing wrong with covering the wound and wiping over it. End quote from al-Mudawwanah, 1/130. See also al-Awsat by Ibn al-Mundhir, 2/180
Al-Nawawi said: The ruling on dressings on wounds is the same as the ruling on splints. … The same applies to putting the skin of certain vegetables and the like on a cut: it is the same as the ruling on splints. … And the same applies to putting anything on the cut, or on cracks in the heel, if it is necessary to put something on them that solidifies.
End quote from al-Majmoo‘, 2/331
You should try to have this “nail polish” applied when you are in a state of purity, so as to avoid going against the scholarly view that doing so is obligatory.
If it is possible to delay using this remedy until the time of your menstrual period, when a woman does not need to do wudoo’, then you must do that, so that your prayers will be offered with complete purification concerning which there will be no uncertainty.
And Allah knows best.