Health and fitness are very desirable in Islam. Our prophet (peace upon him) was very strong both physically as well as mentally. In fact he advised his followers to take good care of their bodies and to strengthen it and their minds.
It is certainly a good thing that boys and girls have separate yoga sessions at your school. Not having separate sports sessions would probably be the only reason why practicing sports of any kind would be forbidden in Islam. I too started to practice Yoga to improve my health and fitness, though I am a male university student and I practice alone.
Whether it is permissible for a Muslim to practice Yoga or not is a very controversial topic actually. There are people who think that it is a good thing and there are people who think it is not allowed for a Muslim to practice Yoga at all. When people argue that it is forbidden they mention Hinduism and Buddhism because Yoga originally involved worshiping Hindu gods. While this is true it doesn't always apply. Today Yoga is mainly practiced to stay healthy, at least in the countries where we live. When I would take Yoga classes here in Germany Hinduism and Buddhism is rarely mentioned. In fact, most of the elements that are connected to Hinduism (and parts of Buddhism) are simply not taught because it would be strange for most of us.
So my conclusion is that I could not find anything that would forbid you to take Yoga classes in school as long as they focus on health, sports and fitness. There are probably more reasons in Islam to do it than to not do it. I mean we are not talking about dancing or anything like that. As you said Yoga does have many benefits for your body and mind and being fit both physically as well as mentally is desirable in Islam. That's probably also the only reason why you would take Yoga classes anyway. It is not your intention to somehow attract boys by practicing Yoga or worshiping Hindu gods. As long as you intent to practice Yoga solely to improve your health and fitness and stay away from Hinduism there is nothing wrong with it. Having the intention to do something good is important in Islam (and staying fit and taking care of your body is indeed a good thing). Yoga without Hinduism is nothing else than doing certain exercises to improve health and fitness. But like in Kung Fu which has its basis in Buddhism, there are religious exercises and moves that are meant to worship Hindu gods and these should and can be avoided.
Note: I have no idea how your teacher teaches Yoga and how much it involves Hinduism but always be careful and aware that Yoga is connected to Hinduism. You can practice Yoga but you should never talk about things like multiple gods or religious things that are connected to Yoga. I practice Kung Fu and I got advised to be careful as well. Shaolin Kung Fu is connected to Buddhism and a man from the mosque told me that it is a good thing to train your body and practice martial arts but at the same time I should stay away from all the Buddhism. (I recently switched to Wing Chun Kung Fu which has a lot less to do with Buddhism and is better for self defense.) When you have the feeling that certain moves or exercises have nothing to do with improving your fitness just don't do them. You can also ask your teacher to remove Hindu exercises from the training (if there are any). Letting your teacher know that you are Muslim is always a good idea.
I hope I could help you with your question. If you want to read more about health and fitness in Islam take a look at the following link. It also provides some sources regarding health and fitness in Islam: http://www.islamreligion.com/articles/1904/