Shimano brakeset hood model compatibility
The hoods are different for different models of levers, but the ST-2200 uses the same ones as the ST-3300. 

The part you need is Shimano Y-6CU 98040. Ask your LBS to find it for you. Alternatively, you can look for 3rd party manufacturers as well but I doubt they will have something for an entry level part like this. Shimano's documentation indicates that the ST-3400 levers do not use compatible hoods (and the style of the ST-3500 onwards is different).