손대다, 만지다, both has almost same meaning, which means 'touch'. But, there is a slight difference in the shade of meaning between the two words. 손대다 is used on the case of trying to touch without permission or starting something. 만지다 is 'touch'. But, your sentence "더 이상은 내게 손대지마" means "Don't touch me"(더 이상은 나를 만지지마) is almost same meaning. "더 이상은 내게 손대지마" sounds like much stronger than "더 이상은 나를 만지지마". As you know, Korean is interpreted as many meaning according to circumstances.