Look at the differential cover on your rear axle to tell which you have, a Dana 35c or Dana 44. It's very easy to tell...
Dana 35c: Perfect oval shaped cover with a black plastic snap-in plug for the lube fill hole. The first pic shows a Dana 35c.
Dana 44: Kind of an asymmetrical stop-sign shaped cover with a threaded steel bolt in the lube fill hole. The second pic shows a Dana 44.
You are right that neither 35" tires nor a locker belongs on a stock Dana 35c axle, it's not strong enough for either in stock form. The good news is that a Dana 35c can be sufficiently beefed up to support 35" tires and a locker by installing either a Super 35 or C-Clip Eliminator kit that are both made by Superior Axle.