DDD does not exist in professional stores, bra sizes go A B C D DD E F FF G GG H HH etc so a Triple D would be an E cup. But before you decide to shop for a bra you should check how you measured yourself because the method of adding inches to the band size was created in the early 1900's because bra materials didn't stretch so women had to add inches to the band size so that it would be comfortable. Places like VS and LaSenza still do this today because they want to make their customers fit their bras not their bras fit their customers.
The modern method is to take the under bust as the band size and subtract the band size from the bust measurement to get the cup size.
A bra size calculator that does this can be found here at http://www.sophistocatedpair.com/bracalculator.htm
The perfect band size is one that you can only fit two fingers under at the back and the perfect cup one that fits your larger breast and doesn't cause any bulges.
Here is how to take your measurements
find a soft tape measure in inches
take off everything and stand up
use a mirror and stand sideways to it so you can see your profile
measure directly below the bust around the rib cage with the tape measure parallel to the floor make sure that the tape measure is tight but not pinching your skin
this is your band size, don't add anything to it or take anything away, if it is a 38 you are a 38 if it is a 37 I would try a 36 first but you may be a 38, if it is a 36 you are a 36, anything in decimal form then round down, trust me on that one, bra materials stretch a lot
Now write down your band size
for the cup size lean forward so that all of your breast tissue is to the front of your body
measure the same way as for the band with the tape measure parallel to the floor if you stand up but make sure you do this leaning over and measure it across the part of your breasts that 'hang' down the farthest when you are leaning over
while still leaning over record this measurement, it should not be tight, in fact it should be loose just resting the tape measure on your tissue and not compressing it anywhere
this is your bust circumference. Subtract your band size from this number
the number you just calculated is your cup size for that band size, round normally to the closest whole number. one inch difference is A, 2-B, 3-C, 4-D, 5-DD, 6-E, 7-F, 8-FF, 9-G, 10-GG etc.