What you wrote is okay but I think it would be better to say, "so much that it made me sore." Muttquad has listed this as an option.
If you want to include the word 'body,' I think it would be much better if you were to say, "Exercising so much made my whole body sore." You see with this sentence, I think 'body' fits better because you are describing where is sore and it's your entire body. For some reason I think being more specific (using 'whole') makes using 'body' more appropriate. It's just my opinion.
The reason I say this is because when you state it made your body sore, are you just saying that or do you really mean it? Is it some parts that are sore or is it all of you that's sore? Using 'entire' or 'whole' to me leaves no implication. Sometimes we say our body is sore but it might not necessarily mean everywhere is sore. It could just be the legs and abdominals but instead of writing that, we just write 'body' because it's shorter.
Or you can say, "Exercising so much made me sore all over." Oh...Muttquad has also said this I just realized.