I lutera birth control about 3-4 months ago. This cycle my breasts have continued to be sore through the end of my period and they also feel heavy and hard. Is this a bad sign? The veins in my chest and breasts are also more visible through my skin.

Not really. I believe that you are saying that you just started Lutera and are continuing on it, at present. Typically women may experience some breast tenderness either premenstrually and/or when they are new to the pill. Lutera is a 20ug estrogen pill - one of the lower dose pills on the market. You may consider going on a 10ug pill. Did you have a recent weight change - that could account this too.