I find myself in a similar situation so I completely understand where you are coming from.
The best advice I can give is that the label you use to define yourself (whether straight, gay, lesbian, bi, pan, ace, etc) can change. If, at the end of the day, you decide that you aren't bi, no one will call you a fraud. Exploring your sexuality is an important stage in life and you may decide that you are, in fact, lesbian. Or you might decide you are bi, it's really up to you. Another possibility is that while you might be bi, you aren't lesbian either. You may choose not to label yourself, or might find you identify as pansexual or another sexuality. There are plenty of things you can find on the internet with explanations of different sexualities which might help if you decide you aren't bi or lesbian.
If you are bi, then yeah, you're right. Bi people are sometimes looked down upon by both hetero people as well as some members of the lgbt+ community. I don't understand why, but it unfortunately does happen. Fortunately, the vast majority of both the lgbt+ community as well as hetero people accept bisexuality as valid.
If you would like, I could recommend a few movies, tv shows or books which feature bisexual characters. Representation can often help people understand bisexuality and in your case, even if it doesn't necessarily help with your identity questioning, it will at least give you something good to watch/read with lgbt+ characters