<sigh> This is… a tough question.
No it’s not okay for her to say it and she should apologize.
BUT, as someone who has been in almost this exact situation, I can tell you it isn’t the worst thing in the world. My mother is an exceptionally frustrating person when she is upset. She argues over the stupidest things and says some terribly mean things. Things that can cut pretty deeply. I’ve been kicked out of my home for deciding to live in the dorms instead of at home with my parents. I mean… it’s just a defense mechanism on her part. At other times, she’ll be angry at something completely unrelated to me or my sister and will take her anger out on us through words anyway.
This is only really painful during those moments (and when I was a teenager). When I was a teenager, I got angry back and it didn’t help the situation. Now, I speak to her calmly and point out that she’s being wrong or walk away. She eventually calms down and explains whatever was on her mind. And sometimes apologizes, but not often. It’s implied a lot of the time.
a) your mother’s actions do not justify “finding love in other places.” As was brought up in another question of yours, it’s your body and doing things that will hurt it only hurt you, not your mother. Going to a boyfriend for comfort is not the same as sex with a number of men.
b) You need to learn to control your response to your mother. Yes it hurts like a bitch when she says terrible things to you. But you need to keep your eye on whatever future you want for yourself. Allowing these things to pull you down at such an early age will only mess up everything.
While there are situations where a mother really is just a piece of trash parent, I recommend forgiving your mother until you’re 20. The age difference will affect both of you. Hopefully for the better.