I don’t have a good voice. In fact, most of the people around me told me that I sing pretty bad. Could vocal lessons help me?

Everyone can achieve a professional singing level. Of course it will need some patience, faith and the right exercises. And in more or less time, depending on your habits and experience. 

Most people think that they don't have "the gift", so they never bother learning. But the truth is that learning to sing right it's just a training of muscles like in any sport. Problems like not finding the tuning, straining, breathy sound, or experiencing problems getting a high pitch are easy to solve with some determination and appropriated techniques. Once you learn to sing with easiness and naturality, the rest is just enjoying and having a good time!

Every person evolves in a different and unique way. Many think that if they aren't praised when young, or shown an early "gift", then is better to forget mastering something like singing. History is full of cases of people that start learning above thirties (or even forties) and have become a genius. Even there is cases like mine's that I sang like a cat in my teenages, and now everybody is praising me "what an extraordinary voice!" because they hear me mastering my voice with easiness and control. 

Practice dreaming without limits, and forget other's opinion about what you can or can not do!