Question

When do I use Me lavo or Lavarme?

Answer 1

Me lavo means ' I wash myself' and it is present tense
Lavarme means 'to wash myself' and it is infinitive tense

Answer 2

Me lavo is present, as in you're doing it right now. Ex: Me lavo las manos = I wash my hands.
Lavarme is more of a going to do something, in the future. Ex: Tengo que lavarme las manos = I have to wash my hands; Voy a lavarme las manos = I am going to wash my hands.