I think you wanted to make the sentence like this: Housework and looking after the baby tire her every day. I'm not sure this sentence is perfect in grammar, though. lol I'm not English native speaker. The verb 'tire' is being used transitively.

She looks after the baby and does the house work. She gets tired every day.

Is the 'tire' can be a verb in that sentence? 'tires' somebody, can I use it like this?

No, and I can't correct it because I don't know what you are trying to say. Do you mean she gets tired every day from housework and caring for the baby?