I think a lot of the transition process is a wait and see thing, you shouldn't drop it just because someone challenges you, but coming across as confrontational won't help either, you need to take this person with you, help her to understand the real you, the you inside trying to get out and exist, you can't hide away forever, it'll eat you up inside and lead to a lot of damage for yourself and those around you. This may not be what you want to hear but talking about being trans is the first step and it can seem like the rest of the path is hidden or invisible, try and get a referral for an evaluation if you can and keep on about it, be persistant but not aggressive, let them see its not a wad or a quirk or a reaction to something else. It can be so hard to get people to see the real you, many will refuse to see, others will want nothing more to do with you, some people might laugh at you in the street and other public places, it can be a hard and lonely road to walk but getting people onboard with you, giving you support and help will make it that little bit easier, if you can believe in your true self then perhaps you can persuade others to see who you really are too.
