So, long story short. I was introduced to this girl three months ago at a bar by a friend. When I was about to leave the place I said" see you later" she replied that "we should hang out sometimes". The last two months we went hiking and had dinner together and we went to the beach.But, nothing romantic was going on, so I felt like I was so friend-zoned. But,the last week she sent me a message on Facebook inviting me to a baseball game where she would be singing the national anthem. I replied to her message and told her that I had no plans and would love to come. She replied that she is happy that I could make it because her parents were coming and her mom is excited to meet me. So, I was surprised by this. I'm not an American, so I don't know if introducing me to her parents would mean anything here. Also, I don't know if I'm friend zoned or not. Anyways, what do you guys think? Am I friend zoned? If yes, how do I tell her that I have feelings for her?

Its difficult to judge whether you are friend zoned based on an internet post, if you cant figure it out yourself then Im not going to figure out either.
Maybe she likes you maybe she doesnt and you are fucked.

The one advice I would give you is to not tell her you like her straight away because nothing good can come from that, you are just going to put her on a very unconfortable spot. Just make a move the next time you are ALONE with her, try to have some physical contact and see what happens, if she looks akward and unconfortable you will be able to tell.

any example of some smart physical contact ?

I'm so confused...
You met few times and you event didn't try to hug or kiss her???
Ohhh, my...
You make it romantic or whatever, you make things happened, they don't happened on their own.
If you like her you should have shown that already.
You still have chance. As the guy before me said: Don't say it just show it. When you are alone.

_________________
“Poor is the man whose pleasures depend on the permission of another.”
Madonna

We did kiss and hug but never made out. So, how do I take it to the next level? And I'm trying to find out if I'm friend zoned!

Read about escalation and kino.
I cannot tell are you friend zoned.
I think she likes you but you don't know how to escalate.

_________________
“Poor is the man whose pleasures depend on the permission of another.”
Madonna

Damn bro, two months and no intimacy?! Are you straight?

Anyway, the only way to find out is to make a move and see how she reacts. If you are friend-zoned the girl will let you know.