Drug-Resistance is due to the over-use and misuse of antibiotics- patients' expectations that GPs will prescribe antibiotics for viral (pointless) and minor illnesses and patients not finishing the whole course.
In hospitals the situation is then compounded because the patient is really unwell and there are fewer effective antibiotics to choose from - the 'strongest' ones have often got side effects too.
Natural remedies wouldn't as far as I can see, cause resistance, they've been used for hundreds, if not thousands, of years. Honey was used by the Ancient Egyptians!