It is difficult to know for certain without knowing what grade of steel it is. It could be 1090, 5160 or several others. If you know, please post it.
I do not think there is any reason to anneal.
Heat up to red hot and quench. You can try water but it is a very fast quench and can cause cracks. Many springs are quenched using oil followed by tempering.
As a first guess, try tempering in the oven at 400 F for an hour and then slow cool. If it breaks, increase the temperature. If not springy enough, decrease the tempering temperature. If we knew the exact steel grade would be much easier to recommend a heat treatment.
Yes, I am a metalllurgist.