Toyota Repair: 92 Corolla noise

Question
QUESTION: Hi , I own a 92 Corolla with 108,000 miles. There is a humming/singing noise from the car after the car warms up. It is getting louder & louder.  It occurs at all speeds but is loudest at speeds around 50-60 when I accelerate.  The noise seems to change pitch when I come to a stop and the trans downshift.  If i could guess it seems to be coming from the transaxle.  I have replaced both 1/2 shafts about a year ago because the boots were ripped.  If I remember correctly the noise may have started then. Last Jan I had the trans serviced at Jiffy Lube where they did a fluid exchange. After this I noticed the fluid was over filled to I let out fluid to the proper level.  Since then I noticed the pan gasket leaking so I replaced pan gasket and trans filter. Neither trans service helped with the noise & it gets louder and louder.  Any guesses at what is causing the humming singing /noise?    
Bob

ANSWER: It sounds like a bearing noise, most likely from the differential gears.  

---------- FOLLOW-UP ----------

QUESTION: Thnk you very much for your quick return of an answer.  So I am guessing I will take the vehicle in to a trans shop and have the trans overahauled. Or if it is the bearing from the differential gear, do you know if it can be replaced from the bottom of the transaxle wihtout taking out the transmission?   It has been noisy for several months now- if I just ignore it I am assuming it will damage the differential gears. Naturally you dont recommend this , but if I decide to drive the vehicle to the ground - do you have any idea how long it could last?  I am planning on retiring in 2 1/2 months and wont need the car to travel to work.  If I decided to just let it go, could it eventually lock up the differential while I am driving?  I know this is not the best approach to repairing the car correctly, but I am just trying to get an idea of possibly what my options are.
Thank You,
Bob

Answer
Thanks for the update
Unfortunately any bearings inside the transmission require transmission removal and disassembly, the differential bearings/gears can be replaced without completely taken the transmission apart but I would advise against that, the longer it makes the noise the more metal particles will go into the transmission part, the noise will just get louder over time but it should be ok for a couple of months. You might also consider due to the age of the car to try to locate a used transaxle assembly and have it installed, it may be cheaper to go that way instead of having this one fixed, transmission parts are very expensive and most people opt for replacement of a remanufactured unit or a used one. In this case if it was my car I'd put a used one in with at least a one year guarantee.