Asexual a deal breaker for a relationship?

So I am technically still following abstinence till marriage, Because I found it romantic but someone made a comment at work that they weren't convinced I wasn't asexual. So I did some looking and it is true that I don't feel sexually attracted to anyone it's always a physical attraction.

So do I tell a potential girlfriend that I'm abstaining from sex till marriage, but I may also be asexual?
Asexual a deal breaker for a relationship?
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