Since you're only 17, EP, youth is probably the most influential factor in the lack of vibrato issue. You are actually at the best possible time of your life to start developing your voice, as you are physically nearly fully grown and intellectually developed enough to analyze your own actions and experiences and draw conclusions from them.

Vocal coaches don't really teach repertoire; they usually work with singers on their repertoire, listening to the sound produced and giving direction to help the singer improve it. This is done by analyzing how the singer produces her sound and teaching her ways to work her body -- the whole body -- so the sound produced is musical and exciting to the listener, and does not stress the body, especially the vocal cords, which are actually folds of soft tissue, and very vulnerable.

The singers who use vocal coaches the most are those working in the European classical tradition, which requires great strength and control. Those opera singers who crank out four acts of Mozart and then go partying after (that's how they get fat) are actually stronger than many an athlete, with years of demanding training behind them. You don't have to be a lieder singer or an opera star in training to benefit from coaching, however, and only a few lessons can make a great difference. And you might find that the Indian classical song tradition has much the same kind of technical requirements, so you could benefit from the expertise available to you without having to swallow the whole camel, as it were.

Any kind of physical conditioning that emphasizes bodily awareness and all-around fitness will also help, and yoga is as good as it gets in that area.

At 17, you have only just started on the path of song. Happy travelling!