Ruling on wearing nail polish and wiping over it in case of necessity

Firstly: 

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 

Secondly: 

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.