An Introvert disguised as an extrovert

Its been a week now since I finally took one of those personality tests, you know the Myers Briggs one? And I've always been told I'm an extrovert. Plain and simple. I like people, I like getting out and doing things, and not a huge fan of being alone.  Here's the problem.

I'm not an extrovert.

I was kind of surprised, although apparently my sister thought so. But everyone always told me I was an extrovert. So I thought I had to be out there doing a whole bunch of stuff. And so i thought something was wrong with me, that in groups of people I was terrified of having to go up and meet someone new. Maybe that's a shock to people who think they know me. But there are a lot of things that I'll do just because I think I'm supposed to. I actually like being at a party watching people. Getting to know people from a far so I don't have to "meet someone new". I am incredibly observant, I will notice a lot of things that people don't usually, small little ticks about people. Anyway, I'm rambling. That happens. I'm really not that great with words. I don't know though, that might be why I have the problem I do.

All of my friendships are more one sided..

Now don't get me wrong I'm not saying that my friends are bad friends taking advantage of me. They're not. I'm saying I see my friendships as better than they are. I may think This is my best friend, when They might think , "oh yeah, she's a good friend of mine."  Now I realized this a few years ago, so that's not new information for me. I only have about a years period of time that I can confidently say I was my best-friends best-friend. And even now I would classify her as a good friend where she probably wouldn't.  I think I'm rambling again...
So any who, I think a lot of my problem is that most of my friends are introverts. AGAIN, not that they're bad in any way. But I think most of my friends see me as an extrovert and are therefore scared of me. I think in part because At this point I only get to see my kids most of the time and they're the only thing I'm able to keep up to date on so when I do finally get to see people that's what I talk about.
Most of my friends.. well really up until VERY recently all of my friends were childless (not a bad thing. Again, just a different phase of life). So I have found that either my friends are bored by my conversation or they're my sisters or my husband friends who think I'm "so cute" (still a child).
Now that I have come to the realization that I am an introvert a lot of things make since. Like the fact that I am terrified to meet new people, and I don't like being pushy, and I don't want to "bother" someone to hang out with me..
so I get forgotten about.
If you really want to hurt me, forget about me. Don't invite me. exclude me.
I get it, no one likes to be excluded or forgotten. Its human nature. But it strikes me harder than most I think. I think in part because I am afraid to meet new people so I hope that I can hang out with the people I know, and than they hang out without me and I feel unwanted.
I really want to fix this problem. I don't want my kids to grow up having to be they're mothers source of friendship, because in my opinion I'm not supposed to be my kids friend. I'm supposed to be their mother.
I just don't know how to fix it.