Heaps of us have had delays in treatment, for a variety of reasons. A couple of weeks, if it means you have some confidence in your doctor, sounds like a reasonable thing.
I'm glad to hear you are giving the other one the flick if you feel they are not doing the right thing for you. I wish more people would ditch complacent medicos--they are like hairdressers and butchers; replace them if you don't like their service. Sure, there may be the odd specialist out there who has the market cornered, but med oncs are a dime a dozen in the cities.
