If you were getting a whining/whirring then most likley your Front/head pinion bearing is deforming, or its dragging along the race which requires you to replace it; which in turn means your going to have to remove the carrier and have a new bearing pressed on (20 bucks for half-hour labor at the shop i use + 15 bucks for a new TIMKEN bearing and 5 bucks for a new race).
before you just tighten it down. i would recommend getting a new Crush-sleeve, and pinion seal (and some silicone). its not entirly difficult. its kinda tricky though you might want to read some articals on rebuilding a rearend, mainly read the sections about
'setting pinion bearing preload.'
Your description sounds exactly as if the pinion bearing preload has loosend. In otherwords, that nut has backed itself off the pinion gear a little bit.
Basically you should remove that nut (pinion nut). Once you get the nut off you can remove the Flange. You might need a soft (rubber) hammer to remove the pinion flange (what the driveshaft bolts too), but it should just tap right off.
After you have the big flange off there will be this seal. The pinion seal. Your gonna damage it trying to remove it, so just have-at-it with a screw driver and pry that sucker out.
Once you get the seal out you will see this little shim/washer looking thing, Thats your 'oil slinger.' Remove that.. and you should be looking dead at the tail pinion bearing. It should just fall out. If not, you might try prying it out but try not to damage it. I would check it for wear. If its worn then you definatly need a rebuild, since thats usually the last bearing to go in a differential.
Once you have that tail bearing out, there will be this little sleeve, it will be about 3/8 of an inch long with a nice bulge in the middle. Its kind of hard to describe but it fits around the end of the pinion and is directly infront of the tail bearing. When ever you loosen the pinion nut you have to replace the crush-sleeve since thats what holds the preload for the pinion bearings. Otherwise you will be stuck with a noisey, ticking-time-bomb rear-end.
If your bearing looks good, and your comfortable with not checking the other bearings (which they should be just fine) then start re-assembling it. Crush sleeve, tail bearing, oil singlar, pinion seal (put a lil of that silicone around the outter diameter of the seal), the flange and finally the nut.
When you tighten that nut down you are going to have to be extra special to it. Every quarter of a turn you should check pinion bearing preload- you do this by putting an
inlb torque wrench on that nut, and turn the whole pinion. Not just the nut, but the whole assembly, gears and all.
It should take no more, no less then 10-20 inlbs to turn it all. if it takes less you need to tighten down the pinion nut a lil' lil' lil' bit, if its more then you need to take it all apart and replace the crush sleeve.
i hope i could help
heres a good picture to help out