There is, of course, no way to know for sure. These are the questions philosophers have debated for ages. As human beings, we cannot go beyond our own limitations and completely understand ourselves. For example, what if we conducted scientific experiments that purported to show that we have free will? How could we ever know that our reading of those results was not simply predetermined by environmental factors? Thus, we cannot know for sure.
It seems likely that there are some aspects of our behavior that are determined and some in which our will is completely free. For example, our sexuality seems to be determined for us. We do not choose (most people believe) to be heterosexual or homosexual. We also do not choose some aspects of our personality like our temper. We are also impacted by our environments. We may, for example, be encouraged to believe certain things by our socialization.
However, while these sorts of things constrain our behavior to some degree, they do not determine it. A person with a quick temper may have more angry impulses than another person, but they do not have to act on those impulses. We have sexual attractions, but we often do not act on them due to such things as societal pressures. We may be inclined to believe in such things as the superiority of a given race because of our upbringing, but we are not forced to actually act on these beliefs.
Our behaviors are not free from influence, but neither are they actually determined by our genes or our envrionments.