How do I write a few sentences that describe me?

[Kagehina]

I am new here, and I do not know much Japanese, if any at all. So, I have a question: if I wanted to write a few sentences, or a paragraph, about myself (my name, where I am from, what I like or dislike, my family, etc.), how would I do that? I have already tried, but it seems wrong no matter what I write.
For example, if I wanted to say "My name is Bri," I would write 私の名前はブリです。
If I wanted to say "I live in America," I would write 私はアメリカに住んでいます。
Assuming that both of these are correct, how would I write these two sentences together?
I already know that once you have stated who/what you are talking about, you can drop the 私は (I think that is right?)
So, would I write 私の名前はブリです。アメリカに住んでいます。
Or am I missing something in there?
Any and all help would be appreciated!

[shin1ro]

I already know that once you have stated who/what you are talking about, you can drop the 私は (I think that is right?)
So, would I write 私の名前はブリです。アメリカに住んでいます。

You're right.
Another choice will be:
私の名前はブリで、アメリカに住んでいます。
But I like your version. It sounds smoother to me.