you can say in this way "I hurt my hands playing tennis" which is the short form of "I hurt my hands while I was playing tennis"

hello first: hurt would be hurt in past tense second : i think in playing tennis is more correct i hurt my hands in playing tennis

I hurt my hands (by or in) playing tennis' Which one is correct for this? By or in? Neither is a good choice. "I hurt my hands" no such word as hurted no past tense can be applied to being hurt. But it can be applied to being "injured" "I injured my hand when/while/whilst playing tennis" By = that an object called tennis injured your hand as if "tennis" was able to physically attack you and injure your hand. It was you who hurt or injured your hand as a result of playing tennis when/while/whilst or during playing tennis. You will hear people say hurt/injured in playing +(whatever) but it is not a natural way to say it.

English Grammar in Use 4th edition by Raymond Murphy is an excellent book. The paper edition is reasonably priced and there is a PDF floating around the net. Unit 60. You can improve your English by reading more. Unit 68. Joe was playing football. He hurt his knee. = Joe hurt his knee (while) playing football.

You should ask another question to begin a new thread. Why can we add a past tense to injure as in injured, but we cannot add it to hurt as in hurted?, which does not exist as word. Then you will get many people contributing and answering. Also I will have a think and a look around for you.