I have DD boobs as well. Although one is probably a C now :). I have bought some cotton "crop top" type bras from Big W (St Marks brand 2 for $17). They are very firm support and may or may not be suitable once I start radiation because of the firmness. I have also bought a couple of bonds singlets with thin straps (not the type with adjustable straps just ordinary singlets). I have tried these under my bra and they are comfortable but quite long. I think that I will cut them so they fit under the bra and not to my hips as my radiation will be in October/November which is quite warm in Brisbane. Ask your medical staff if you have concerns.
I understand the concern is tight clothing rubbing on the sensitive skin and possibly aggravating it. Also as the weather gets warm allowing the skin to breath and stay as cool as possible.
Hope you find a solution that is comfortable. Take care