Yes, you do have a GT2860RS. It comes standard with a 3" inlet and a 2" outlet, which is what your turbo has. Your turbo also has a T3 turbine housing on it, that was an option for all the GT28R series turbos. It should spool very quickly and pull strong in the upper RPM band. You have a good turbo on your hands!

BTW, just food for thought, not all BB turbos are water and oil-cooled. Some are just oil-cooled... look at the Turbonetics BB turbos. A few other companies are like this as well, such as Comp and Innovative. If a turbo is BB and only oil-cooled, it normally means it has the ceramic BB center center. It can withstand heat alot better than the standard BB center section... it is more advanced turbo technology.