was doing my wadoo and i was entering water in my nose and i felt that it is dry.I didnot sniff but took a little more water,more than that i took on the first and second time and it entered my throat through the nasal cavity. is my fast valid?

I am keeping up the missed fasts of ramadan.One day i was doing my wadoo and i was entering water in my nose and i felt that it is dry.I didnot sniff but took a little more water,more than that i took on the first and second time and it entered my throat through the nasal cavity(1 or 1.1/2 drops). I did wadoo2 times for namaz e zuhar and asar and it happened both times. Now i started to have a feeling that my fast is  invalidated.My question is that was my fast broken?

The second point(and here i am confused alot) is that to ensure that i am not deliberatily letting drops enter my nasal cavity.I tried to put water in my nose 3 times as in wadoo(but it wasnot wadoo). Again one drop entered my throat.At this time i feel to realize that my fast is invalidated because i read in behasti zewa! r that when you vomit and feel that your fast is broken and then eat something knowingly over that then the fast is really broken.