Shoes or no shoes?

Hiya guys, I was wondering to buy taekwondo shoes or not

My master allows them but we take them off for sparring.

I practice WTF Taekwondo in a church hall which has wooden flooring, but after each session (about 2hrs) my feet are horrible, I even got a cut last week.

I also find it difficult to pivot sometimes due to friction on my feet and the floor. Would shoes make it easier?

Lastly, could I wear the shoes to walk to taekwondo instead of bringing two pairs of trainers?



Thanks everyone!