Right, the shoulder straps are falling down because the band is too big.
Your measurements suggest a start point of a 34GG.
Now, Ebay buys when it comes to bras can actually be very dodgy. The big bra companies have factory outlets where they sell reduced stock - but at least some of it is mislabeled/mismakes etc. Not all, but some. I suspect you can guess where it ends up...
Going from a 38, a 34 is going to feel tight to begin with, but it will fit you. Your band should be taking the vast majority - say about 80% - of the weight of your breasts. It can't do that if it's 4" too big.
Also, its very very important to scoop, especially when you first go down to your "true" size. Breast tissue can migrate under your armpits/towards your back and this is especially likely if you have been wearing ill fitting bras. When I first put my bra on, you'd think I'd never fill the cups and that the back is snug...but it's not.
Grab those 34s (and tell us what they are). First up, put them on back to front. This will let you check how the band is. You should be able to pull it a couple of inches from your body. That's it.
Now, take it off and put it on the right way. TO do this, put the straps on, lean forward and pour your boobs in to the cups. Then fasten it up at the back. Now, stand side on to a mirror. Take your left hand and reach round inside the right cup. Reach round as far as you can, so your hand is all the way under your arm (your fingers might well reach round your back). Now pull forward all the soft tissue you can feel - you basically want to manhandle it forward in to the cups.
Repeat on the other side.