[A4] Uphill troubles

[Go Cubs]

Hi,
Hoping I can get some advice. First, let me say I not much profiicent on 
cars so bear with me if I sound foolish.

I've an 98 Audi A4 1.8T, 85K miles, manual transmission.

Over the last month, when I've changed gears, usually from 3rd to 4th or 4th 
to 5th, the RPMs shoot up (without speed shooting up) and then go back down. 
I've noticed this happening when I'm going uphill, even slight though long 
uphills.

Just yesterday I drove a long gradual uphill in 2nd gear and I had a tough 
time getting my car to accelerate. After I stopped there was a burning smell 
(from outside the car).

What could this be??

Thanks

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