Whining sound from front engine.

Hallo folks. My Audi 2002 A4 1.6 which I own since four months ago it developed whining sound or like metal to metal sound when shifting to 3rd, 4th gear and while accelerating up hill. Since I bought the car I changed the timing belt and the water pump. The car was in service one month before I bought it. They changed the spark plugs, oil, oil filter, hydraulic fluid and brake fluid.

The car was perfect and still rides perfect. Except this annoying sound that irritates me. It happens a lot only when the weather is hot. I've been to Audi Dealer in my city. I explained the situation. I got to be told it might be the gearbox. I made appointment this coming Friday which I cancelled cause they are demanding a lot only to check what the problem is.

The whining sound happens only seconds when going uphill especially when the weather is hot! If the problem is the gearbox shouldn't the sound come under the stick and not from the front engine?

I'm planning to go home (The Netherlands) in the coming summer to fix the problem. Cause here (Norway) the price they are asking is insane! I was told should the gearbox be the culprit it's gonna cost me €7500 which I didn't paid to buy the car itself. Should I be okey to use the car for the next two to three months? I've been driving with the same problem since a month ago. Thanks in advance.