If DD is used to you almost never wearing makeup, the "change" may have been hard to handle and she may have just snapped out something rude and thoughtless.
I used to hate seeing my mum wearing makeup and I remember a few times telling her she looked horrible! I was a fair bit younger through, probably 7 or 8.
Do you know what shape your face is? If it's square jawed then you might just possible have some facial characteristcs that are usually thought masculine. For example if you have a strong jaw then a bright lipstick might not suit and you'd be better with something more neutral.
If you go on YouTube (I'd have personally rather died than go to Boots and confess my makeup ignorance) and search for "find out your face shape" and then "makeup looks for [my shape] face" you should get some good tips.
I now wear very minimal makeup but enough to show that I've made an effort, IYKWIM. No foundation or powder (I've not found a single one that doesn't make me break out in pimples after using it. I do get rosacea sometimes so I do keep a bottle of Dior's Airflash (which to me is ludicrously expensive, but I use it so infrequently that I can justify it, just for those ocassions where I'm about to go into a client meeting or something and just need something to cover the redness)) Eyeshadow (I use a ELF palette which I got in Superdrug for about £5, I think it's called Shimmer Shine.) Eyeliner - I like to use a liquid pen, in the past I've bought GOSH at about £7 but right now I'm using a Garnier one which was cheaper and seems to last longer. Then finally a GOSH eyebrow pencil. I tend to just put lip balm on, so don't bother with lipstick.
I wear this during the working day 5/6 nights per week and my eyeshadow palette and eyebrow pencil have lasted just over a year so far :D It takes me 2 minutes to put on.
I'm sorry you felt so hurt but I hope you enjoyed the theatre anyway. I defo think you need to talk to your DD though. She must understand at 11yrs that this kind of comment just isn't ever right. It would still have been honest of her to say "I don't like it" but "you look like a man in drag" is very tactless. If she talks to people at school like that, she soon won't have any friends!