What Surgical Procedures Will Correct Weird Shaped Breasts?

It sounds as if you have a condition called constricted breast or tuberous breasts (some people incorrectly refer to this as tubular breast).
There are many options that have been discussed for management of this. You may want to look this up on the internet.  Many surgeons will use a combined approach.

Good Morning,
From your excellent description it appears that you have a a tuberous breast deformity. This is a condition in which the breast (or breasts) are very narrow at the base (as if you placed a rubber band at the base of your breast and the breast itself was squeezed tightly) causing the breast to appear droopy and the areola to appear very large. This can corrected with surgery that will release the constriction of the breast and reduce the size of the areola improving the breast shape and improving your breast symmetry. This procedure is often accompanied by a breast augmentation to help expand the breast and give it a more natural shape.
I hope that this information helps you.

By the description you wrote, it sounds like you may have a tuberous breast or a constricted breast.  This is a condition where there is a narrow breast with tight lower pole and often herniation of the areola.  This can be corrected with surgery.

Dear Anonomous Girl,
By your description you have what is referred to as a tuberous or constricted breast. This is not really all that uncommon and there are surgical procedure that can help improve your shape. This can be done with and without a breast implant.
Your best starting point would be to do a google search on thberous or constricted breasts and see if that matches you.
Your next step will be to meet with a board-certified plastic surgeon close to you who can examine you and review the options available to you.
I wish you well.
Dr Edwards

Dear Anonymous:
This is a common complaint. It sounds like what you have is a breast asymmetry with I think a tubular (or tuberous meaning potato, but everyone hates that terminology) breast deformity.
With a tubular deformity the breasts have a very tight inframammary crease and the nipple areolar complex may be very protruding. In some cases the breast almost has a tightness all around the base of the breast. This is often treated by doing internal work on the breast, and placing an implant. Most of the time a peri-areolar breast lift is performed at the same time. It does take time for the breast to settle and touch ups are common.
As far as the asymmetry all this means is that you may need different procedures on the 2 breasts. One may need a lift plus implant one may need only an implant.
Seek a doctor with experience in this type of surgery. You are located in Dallas and there are many fine surgeons in Dallas with a great deal of experience in this type of surgery. Go on several consults before you decide on one.
I wish you good luck should you go ahead with surgery.