What the next bra size after 38d?

The next bra size after 38D is typically 38DD (or 38E, depending on the sizing system used). In general, bra sizes increase in increments of one cup size for each letter, so moving from D to DD (or E) represents the next size up. Additionally, you could also consider going up a band size to 40 to see if that offers a better fit, which would then correspond to a D cup as well.