Q: ipod touch won't update

The 2nd gen can only go to 4.2.1 so you can't download apps that require iOS 4.3 or even 5.

https://sites.google.com/site/appleclubfhs/support/advice-and-articles/finding-a pps-for-older-devices

You can find apps that are compatible for iOS 4.2 or lower. Can't go beyond iOS 4.3

Check your iTouch. Since you said

The ipod is only on 2.2 right now but doesn't seem to go any further.

You could have a 1st gen (not sure, just guessing).

Identifying iPod models

Ok, you could also have a 1st gen. Those can go to 3.1.3. But you have to buy the update to 3.1.3. (few dollars i think)

support.apple.com/kb/HT2052.

Do you have button for the volume control on the side of your iPod? If no, it's a 1st gen.

A 1G iPod can go to iOS 2.2 via iTunes and iOS 3.1.3 via

Purchasing iOS 3.1 Software Update for iPod touch (1st generation)       

https://buy.itunes.apple.com/WebObjects/MZFinance.woa/wa/touchLegacyLandingPage

A 2G to 4.2.1. Requires iTunes version 10.X. If a Mac it requires OSX 10.5.8 or later.

The 1G does not have volume buttons on the upper left side.