I am also a second year medical student, and I also used to face the same problems that you do.
The meditation practice of 'Anapanasati' will allow you to sleep less and focus more. For instructions on how to practise it, follow this link: https://www.youtube.com/watch?t=206&v=YKFl4E3YhlI
Practising this meditation makes your mind calm, concentrated and will give you a lot of mental power. The strength and the duration of these effects are dependent on how long you practise (a session of 1 hour would be optimal, but feel free to get up and go if you wish to before the full four), how frequently you practise (at least twice a day would be optimal), how regularly you practise (try to stick to the schedule as best as you can), and the intention with which you practise (intend to let your mind become calm and concentrated). This practise of Anapanasati is exactly for this purpose of building attention and eliminating any stress you have, and it is also very powerful at accomplishing this purpose, provided you practise correctly and appropriately.
If you practise this meditation appropriately, you will find that your attention will grow rapidly and that your stress levels will be non-existent.
You will also find that you will have a lot more free time, because your elevated attention and non-existent stress levels allows you to get a lot more study done in much less time.Because your mind is very calm (since practising this meditation will declutter your mind) as a result of successful and appropriate practise of this meditation, you will find that your sleep will become very deep, and so you will not only need less sleep but you will also be much more refreshed.
The video that I linked to you that has the instructions on Anapanasati may seem too short, and not very comprehensive. But my advice to you is that comprehensiveness of instruction is not at all the key to success in this meditation, and not much more than what he says in the video needs to be known for successful practise of Anapanasati. The key is to be persistent and stick to the breath as much as you can, and gradually your concentration, calm and mental power will develop.
Although what I am about to say may cause some amount of sensation to arise in people who are attached to their insight meditation traditions, I would advice, from my personal experience, that you don't practise insight meditation exclusively (the anapanasati meditation that I recommend is not an insight meditation, it is a calming meditation) since it will cause many troubles, especially in a student life like ours. This is because exclusive practise of insight meditation will initially cause many defilements to come about (although the goal is the contrary) - for example, all kinds of craving will come about. This is not conducive at all to a successful student life.
You can, however, practise insight meditation during daily life (rather than the main meditation practise) such as while walking and eating and so on, without getting into much trouble, ASSUMING that you have a solid practise of Anapanasati going on.
I said earlier in the post that a sitting session of one hour at least twice a day is optimal. This might seem too much in the beginning, but the effects of sticking to this regular schedule will change your life so much that you will find that it is not too much at all, given the benefits that it provides you, and you will find that in fact it gives you a lot more free time than before.
To clarify what I meant by insight meditation, it is the exclusive practise taught by the Buddha whereby you will be able to understand reality clearly and therefore be free from suffering. Here is a manual on how to practise insight meditation, written by a great monk called Yuttadhammo: http://static.sirimangalo.org/howto/HTM.pdf
My addition of insight meditation here may seem irrelevant to your question, since Anapanasati is the exclusive answer to your question, but I am assuming that you understand the doctrine that the Buddha taught and that you have set yourself on the path to freedom from suffering. So do bear in mind my warnings regarding insight meditation in the context of student life, so make sure that you are only practising Anapanasati during your sitting meditation session, and practise insight meditation during your daily life to the best of your ability.
You will find that if the calming meditation (Anapanasati) and insight meditation (the exclusive practise that the Buddha taught to be free from suffering) are practised together in the manner I described above, insight meditation will not only no longer be a hindrance (because your mind has become powerful and stabilized by your solid practise of Anapanasati, you won't be overcome by craving and other defilements) but it will support your Anapanasati practise, which in turn will support your insight meditation practise as well. In fact, the meditation schedule that I prescribed to you seems to be also what even the Buddha seems to have taught to some people on a certain occasion, where he provides instructions on both the Anapanasati meditation and the insight meditation (traditionally known as the practise of 'Satipattana').
Feel free to ask for any clarifications, I hope what I said makes sense to you and that you too will be able to solve your problems.