With lots of work and money, you can turbo your 22re, toyota even built a 22r-te that was turbocharged from the factory.
Now just cause you can do something does not mean you should. It would be alot of work to +t your engine for little gain. The 22re is a great engine, however it is not a very suitible performance platform. IE longstroke bad for high reving and sohc 8v bad for flow. By the the way this project would be very extensive in work and parts and you would still be slow.
If you are serious about tuning your celica, you should consider an all out turbo engine swap along the lines of 7m-gte, 1jz-gte, or 2jz-gte (listed in order of cheapest to best performing). Your car is a perfect canidate for one of those swaps.
It sounds like you got lots of learning to do before taking on a project like that and expect to spend lots and lots of money and then some more money. Custom cars are an expensive habbit my friend. Goodluck in your quest for speed.