Suggestion
We need to know exactly what you are running, and how you have your stuff set up. Most Honda turbo kits are supposed to come with a MAP bypass valve, sometimes called a "check valve." This prevents the ECU from seeing boost. Also, they usually come with a rising rate fuel pressure regulator, sometimes called an "FMU (Fuel Management Unit)." You need to tell us how you have everything hooked up and what parts/accessories you have installed on/in your motor.
Also, based on what I have read so far, it sounds to me like you have a timing issue. I have a turbo B16, and I dove mine for over 5,000 miles before I got it tuned or chipped. It ran super rich, but it didn't back fire. Don't waste your money taking it to a shop that will charge you $60 to set the timing. Based on what you're telling us, it sounds like you're just having a timing issue.
Double check all your turbo parts according to the manufaturer's specifications, and make sure that you installed everything correctly. A mixed up vacuum line or timing too far advanced will cause you a lot of problems.
Based on the white smoke, it sounds to me like you have the timing too far advanced and you are getting detonation which has likely blown your head gasket, expecially if you have been exceeding about 4,000rpm.
If I were you, I would go to autozone or kragen or pep boys or whatever, or better yet, borrow a buddy's timing light. Make sure you set your timing to zero! If you are unsure how to set the timing, refer to a service manual. This is a 5 minute job that every shop will rip you off for at least $60 to do. SAVE YOUR MONEY!
Setting the timing and double checking all your turbo connections should at least get you to a point where you're not damaging your internals every time you drive your car.
As far as tuning your car, just upload a base turbo map. They are generally very conservative and rich, which means that they will not make much power, but it is a very safe map to use until you can afford to get your car tuned.
In summary,
1. Set timing - Cost: $0
2. Double check all vacuum/turbo connections - Cost $0
3. Running your engine with the timing too far advanced without a tune plus boost - $priceless
Good luck buddy