YOu may be running in the wrong sort of bra. Most running bras are "compression" style - which basically suck it all in, in one not-so-glamourous bulge. This, of course is fine for A or B cups, but not for a D cup.
Look for a sized sports bra, called "encapsulation" bras, which basically will treat each breast as a separate unit and support them equally. This is different than the S-M-L sizes you will see on compression bras. Many encapsulation bras are sized as double sized eg. 34-36 C /D. Champion, New Balance, CWX, and other companies make excellent versions of these bras. Some women will prefer these to fit a size smaller than their regular bra to give them a little more feeling of support.
Bras are a very personal thing. I know many D and DD who are very happy in a compression bra, and B cups who will prefer a full on encapsulation.
Key features to look for, if you can't find the "brands" are:
NO cotton - cotton in running clothes is bad, but in a bra is terrible. Cotton fibres stretch as they become wet, so you will get less support as you go along
Adjustable straps
Multiple adjustments on back
Cross straps (some prefer this) - less pressure on shoulders
Plan on spending some serious time to get fitted properly. Wear your running shoes, and jump up in down or, better yet, run with the bra in the store. Don't get stressed and take the time - it will be worth it SO much in the end!