Without ever having tried BJJ, my impression is that it's totally normal.. every time you start something new that implies new physical skills, you suck for a few months. We all did in our respective arts.
The main difference here is that you're immediately put together with people who have a slight advantage over you.
As for the three minutes - yeah, I find BJJ boring as heck to watch which is why I am not that interested. You could pick up Judo, it's a bit more lively.
You mention you're getting drained... there already you have a key. Obviously you're relying too much on physical strength. The idea of any martial art is that you don't need to be all that powerful and fit. It is useful but not necessary. Technique and understanding of body mechanics beats strength and size (but you gotta be good for this latter
), that's the whole idea.
Instead of trying many moves, you could agree to practice a single technique with a knowledgeable partner: he will let you get in a position where you can try it - and it must work without big exertion. Agree on a "freeze word", so you both can stop "fighting" and you can examine your position and your partner can give you advice, then you restart.
The key is to not give up.