Bhí náire orm.

I was ashamed / I was embarrassed. Both? How can you tell the difference? It may not always be obvious by context.

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I think they overlap in most languages. How exactly were you trying to distinguish them in English? Do you have some examples where one couldn't be substituted for the other? (I think of "embarrassment" as the "seizing up, etc., that results from feeling shame")

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Múinteoir Gaeilge - Irish Teacher
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect, but I can also speak Ulster and Munster Irish with native-level pronunciation.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), Gaeilic Uladh (GU), Gaelainn na Mumhan (GM), agus Gaeilge an Chaighdeáin Oifigiúil (CO).

I was presented with an award - I was embarrassed to be the centre of attention (proud but embarrassed) whereas I stole money and was ashamed (not just embarrassed) of myself for doing it. I think to feel shame is different to feeling embarrassed although I understand how sometimes both might apply.

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I think náire would only apply to the latter not the former, then. (Unless others step forward to disagree. )

Perhaps:

Bhí cotadh orm. I felt embarrassed/shy (because of all the attention.)

But there are a few other words in the vicinity that might suit the situation better. Await further input ...

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Múinteoir Gaeilge - Irish Teacher
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect, but I can also speak Ulster and Munster Irish with native-level pronunciation.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), Gaeilic Uladh (GU), Gaelainn na Mumhan (GM), agus Gaeilge an Chaighdeáin Oifigiúil (CO).