I've worn contacts since I was 10 or 11. My dad just recently retired from optometry. I worked for him for several summers, so I have a bit of knowledge on the subject...
Toric is the type of contact that corrects astigmatism - not a brand - almost all brands have toric lenses. You very well may have two different brands, but I would question why.
Did the doctor just not have your prescription in the trial pair for the eye that needed the toric lens? Or is he/she planning on putting you in two different brands permanently?
Also, I will assume that the doctor or his assistant taught you how to place the toric in your eye correctly. There is a top and bottom to toric lenses. If they did not give you specific directions about how to place the toric lens in your eye, then that could explain why you're always feeling it - it's not sitting on your eye correctly. It could also be "turning" on your eye throughout the day if they don't fit well enough.
The Acuvue Oasys toric lenses have single "dashes" on the top and bottom. Those dashes should be vertical when you place the contact in your eye. Other brands/lenses have three dashes that look sort of like sunbursts on the right and left side of the lens, and those should be horizontal when you place those on your eyes. Different brands have different marks and different ways of indicating how the toric lens should be worn.
Also, this is why they have the trial lenses - to make sure they fit and you can function with them before they finalize the prescription and before you spend a lot of money on contacts you can't wear.
Call your doctor. Tell him what's going on. He may tell you that you still are in the adjustment period, but I would bet he's going to have you come in.
Oh - and yes, your eyes will feel tired later in the day. Most doctors will have you start out wearing them for only a short amount of time each day and then extend the time either each day or every few days until you're wearing them a full day.
It's starting to sound like your doctor or his assistant didn't give you the necessary information to be successful adapting to these...