This is weird. I was in an dream inside a dream. When I was in one dream I was puking. Then I woke up and I was in a different dream all in one. My sister said while I was in the other dream that I was going to puke and I did. But I find the Dream Inside Another Dream interesting. 
I am pretty sure what you experienced was an FA 
Is all that we see or seem
But a dream within a dream?
Edgar allen poe
So anyways
yea fa
not all that uncommon
it is cool, though i hate them
If we wake up we’ll remember it was all only a dream
yes, the dream-inside-the-dream is interesting 
I had one like that last night. So funny when you wake up. I really thought I was awake when I went to sleep in that dream. And I WILDed incredibly easy 
It seems there are two variants: one where you wake up inside another dream (can also be a false awakening if you think you are really awake) and one where you go to sleep in the first dream ending up in the second one.
when you woke up in the second dream, did you think you were awake or did you know you were still dreaming?
It’s getting interesting if in second dream (that one inside first one) you are getting lucid. Then you have to guess that first dream was reality or dream. That’s always confusing a bit, even more if in first one you WILDed or MILDed. 
yes indeed. In my dream last night i really thought i went to sleep in reality although it was a completely strange setting. When I woke up for real i realized i was already dreaming when I went to sleep. Duh, and I even plugged LD4all to a DC when going to sleep and told her: i’ll make you lucid when we are dreaming"
Quite a while ago, I dreamt that I was having a LD, then I woke up (in the dream) and carried on with the dream. At the time, I was really excited because I was getting closer to having my first LD.
i have had that happen before… it was a dream and then a false awakening…
in the dream withen the dream my room was full of spiders
scarrry
i woke up and thought it was over and i got out of bed and there were still spiders everywhere 
I’ve had a couple of those, they’re usually a lot more simplistic then my regular dreams…
Lol, i hate spiders also. That sounds funny though.
Kinda like, Deja Vu… I had Deja Vu in a dream last week and let me tell you it was SO BIZARRE. I couldnt tell what had REALYL happened. I was so convinced that at the bar in the dream with certain buddies had happened before. So I experianced deja vu, in a dream. Its so weird.
As others have said, I believe you had a false awakening. 
They can be fun, especially if you become lucid during them, but annoying if you write an entry in your dream journal as soon as you wake up, only to find out that when you really wake up, you have to write it all over again. 
A good way to prevent that, is to make it a habit to do a reality check (or two 
) as soon as you wake up. That way, you’re very likely to become lucid in any false awakenings you might have. 
I had an odd dream one time, that in my dream I went to sleep. As soon as I fell asleep in my dream, my point of view changed, so I was watching my sleeping self lie down on the bed in my dream. Then I apparently started dreaming in that dream-- there was a little thought bubble above my head so I could watch what I was dreaming about. Confusing, but fun. Never got lucid in that one though.
I had a FLD inside a ND once.
I was sooo mad when I woke up. 
I’ve experienced that before, and it’s really weird. I was having some kind of ND (I don’t remember what it was about) when I had a FA. I was in bed and I remembered the earlier dream, and I was reaching over to turn on the light so I could write it down when I “fell asleep” again and entered another dream. It was weird.
a play within a play, hamlet, anyways yeah i’ve had that before. I was so mad, 
Like Edgar Allan Poe - Dream within a Dream.
I’ve had one of these before. In my dream I was at school and sitting on the curb of the bus circle waiting for my bus. I somehow fell asleep and “dreamed” that I was in my mom’s truck with a friend playing my Gameboy Advance SP. Though, I think I fell sleep in the truck and woke up freaking out at school because I thought I missed my bus (I always fear being late).
I think that’s only one I remember.