Assalamu alaikum brother!
You mentioned two things. Ghusal (shower) and Wadu (ablution).
If shower was fardh (obligatory) on you, then your ghusal and wadu are both incomplete without washing your nostrils.
But if your ghusal (shower) was not obligatory, then it was ok if you missed washing your nostrils. As nostrils are not Fardh (obligatory) in wadu, but it is Sunnah. Which means, if you miss a sunna in wadu, it is still acceptable.
I would like to mention what are the Fardh (obligatory washings) in Ghusal and what are Fardh in Wadu:
Fardh in Ghusal:
1- washing of mouth
2- washing of nostrils
3- washing of the entire body
Fardh in Wadhu:
1- washing hands upto and including the elbows
2- washing face (from where the hair grows on the head upto under the chin. And from one earlobe to the other earlobe)
3- doing mas-ha (touching with wet hands) of at least one fourth (1/4) of the head
4- washing feet upto ankles
Note: If you miss a Fardh in either Ghusal or Wadu, it is not standing.
I hope it helped.
Wassalam