What car do you have?
Yes, your tire size is too narrow for the 8" wheel.
Where do you live and is there a reputable tire shop in town?
Our sponsor, Tire Rack, has a function on their site which will give you proper sizing options for either factory sizes, or plus sizing applications(16, 17, 18").
http://www.tirerack.com/tires/...=1992Since you supplied no year, make, model, I assumed you have something similar to a common '92 240 fastback.... but please take the time to plug in whatever specifics you can, and Tire Rack will spit out proper fitment sizing for you. It really is that simple.
A tire has a range of wheel widths that it can work within. When you "stretch" a tire to fit a wheel, you're asking the tire to work outside of it's designed functional parameters. This leads to premature failure of advertised tread life and casing and/or sidewall construction.
Also, as you have found out, this stretching will allow damage to your wheel, as it is now unprotected by the "rim protector."
Check Tire Rack for proper OE fitment, and check closely at their recommendations for 16, 17, 18" sizing. They know their stuff.
Also, look into getting some narrower wheels. 7.5 is maximum that I can find Tire Rack recommending for the car I have to assume you're talking about.
This 7.5" recommendation falls in line with one of the Bridgestone/Firestone website's tire spec sheets. Couldn't find a Dunlop spec sheet quickly enough...
http://www.bridgestonetire.com/dpp/
My guess is most tire manufacturers will suggest at least a 235 width(to cover their arse), for such a wide wheel.