the major concern with injecting anything into the breast area is : infection. Bypassing the skin (natural barrier to infectious particles), you may accidentally induce bacterial growth inside, and get a very bad infection, no matter how clean or sterilized you may think you have made things. this is why most injected materials are done in clinical offices or hospitals. you can risk even getting a staff infection (very bad indeed). near fatal in most cases, if caught too late, or even septsis. Mastisitis is very likely (infection of breasts). if untreated it may become gangrenous and will have to be surgically removed.
the other concern would be: where to exactly inject it.
With the amount of blood vessels and lactiferous ducts (milk ducts) that are in the breast area, you risk perforating (puncturing) a vein or injecting that material into an artery or lactiferous duct.
Hyaluronic acid is hydrophilic : it absorbs water. Some sites claim it can absorb up to 1000x its weight in water. imagine that being injected and all of a sudden, it is a lump, that gets bigger. no even counting infection...
there are also a matrix of connective tissues within the breast. so it would likely not even spread evenly.
There are people who inject saline (not advisable for reasons mentioned above), to give themselves a breast lift /temporary augmentation. Even though the body contains saline (think of your tears), it is still the same situation, the matrix prevents an even flow, it has to be absorbed throughout the tissues.
So besides all the medical input, there is also the visual appearance. will it be lumpy/uneven?
is it even worth the risk? not for me.
your body is like Lego's, with the right building blocks and imagination you can build anything!