trannys are hydraulic in almost every function...if the fluid level is fine then the whining could be coming from one of the planetary gearsets.
The first order of business will be to change the trans fluid and filter. When the pan is removed you'll be able to tell if there is a great deal of residue or metal shavings in the pan. There is magnet in the pan put there to attract any metal filings, a little is to be expected but alot will signal major damage.
If you dont have the tools or place to do this on your own then have a local shop do it. Just make sure you insist they pull the pan off and change the filter. DO NOT let them hook up one of those pump-n-flush machines!...if youhave an internal pressure leak the power flush will just make it worse. Flushing is fine on newer cars but not high mileage. This is not to say this will fix the problem but it may buy you some time and it will show if you have major repair issues ahead.