Can I use Canon EFS 10-22MM USM Wide Angle Lens on a t3i?
Yes. The dRebels can use both EF-S and EF lenses. It's the full-frame bodies (5D/6D) that can't use EF-S lenses.
That's up to you. The EF-S 10-18 costs a lot less and does most of the same thing. If you plan to pair it with a 24-105, it overcomes the 24-105's greatest weakness on crop, which is that it doesn't go particularly wide unless you're on full frame.
But if you wanted to go faster (say, shooting environmental portraits or architecture from indoors), then a Tokina 11-16/2.8 might be better.
and I just recently bought the canon 24-105mm ef stm lens was that a waste on a t3i?
That's up to you. I used a 24-105 on an XT and loved it, but only realized what it was supposed to be when I got a 5DMkII. If I were staying within the crop world, an EF-S 15-85 might have been a better choice.
I was always told upgrade lens not camera...I hope I made the right decision.
It depends on you, your budget, what and how you want to shoot, and what it was, specifically, you needed to upgrade. Sometimes it's the camera; sometimes it's the lens.
The main reason folks advise the lens in the face of no information about the other factors is that you tend to swap bodies at shorter intervals than you swap systems or formats, so most lenses stay with you longer, and therefore have better resale value (less depreciation).
Also, the time to ask about lenses is probably
before you buy them.
