No, straight people feel no attraction to the same gender. I can see why you would think that. Many people think or say they're straight, when really they identify that way due to societal pressure and expectations, not because it reflects their actual feelings.

Lesbian is a label for women who are only attracted to women. I wouldn't use it unless you're sure you aren't attracted at all to men.

You don't have to know what you are right away either. For now, I think bi fits you as a label, as you say you are attracted to men and women. Even if you are more attracted to women, like I said, that's normal for a lot of bi people. The bi label totally contains all different types of levels of different attraction.

If it turns out later that you are a lesbian, that's totally fine! Use whatever label is comfortable for you, and accurate to your experiences. Or, like the previous poster said, you don't have to use a label at all. What's important for right now is that you accept and explore your feelings.