There's three possibilities here--
Either Keira is right and your bra isn't the right size or your corset is doing things it shouldn't, or both. Although the corset is really just doing what it's designed and built to do-- hold certain things in place *quite* rigidly.
Anyway, I guess you're wearing an underbust if you have a bra on. If the corset is more than a waist cincher (i.e. a longer corset that maybe stops just below the bust) then it's going to push on your bra band, and your breasts (primarily when you bring your arms back down from reaching overhead). By stretching upward, your torso and bust can narrow a bit, and then as you bring your arms back down, your breasts and bra aren't going to settle right back in the way they were. Hence the need for all the uncomfortable adjusting.
To see what I'm talking about, try standing in front of a mirror with just your corset and bra on. Reach up, and see what happens. The corset doesn't move since it's anchored at your waist. Everything above the waist moves as you reach. Now as you bring your arms back down, you should see where your problem is. The bra band is possibly getting caught on the upper border of the corset.
Solutions--
1. fix your bra size issues (if you have any)
2. fix your corset issues. Probably not size related*, this is mostly just an issue of making sure you have the correct foundation garment on for what you're doing. A long corset isn't going to be good for the type of activity you're talking about (i.e stretching/reaching overhead). Now, I'm assuming you're dealing with a longer corset, otherwise you wouldn't have brought it up. If you're short-waisted and just wearing a cincher, it's going to be the same problem. So, in order to not mess up your bra situation, you'll need a shorter corset.
2.a Alternatively, you might consider a good girdle or other bit of shapewear. Something that doesn't cover as much of your torso is really what you're looking for, or else you'll have the same problems as you do with the corset.
Anyway, hope that helps. Let us know how things turn out! (or have turned out since this is a bit old)
*Shortening the chest measurement to get a more snug fit around the upper part of your corset won't work because you'll still have the same trouble when you reach overhead--the corset only anchors at the waist. That's where the main reduction is occurring. The chest measurement should be snug, but you aren't cinching your lungs.

Alternatively, leaving the upper part of the laces a bit looser won't work either. As the day wears on, the laces will sort of re-adjust and re-distribute in such a way that any slack will be more evenly distributed. If you don't believe me, try lacing in an hourglass-- very narrow at the middle, wider (almost loose) at the top and bottom. Go and do some normal stuff-- bake a cake or whatever. After a few hours, the slack from the top and bottom will have worked their way into the middle, and the hourglass shape will be gone-- the rear busk (if your corset laces in the back) should be straight up and down-- perfectly vertical.