I am sorry to hear that. But i don't think one can put contact lenses into eyes rightly just with only one hand. If you really need contact lenses, you'd better ask your families or your friends to help you put in the contact lenses. If not, you are suggested to wear prescription eyeglasses. Trust me. this is a good way to solve your problems.
Actually, I'm sorry to hear that, hope your hand get recovered in no time. Ok, currently, you cannot use another hand, and you don't have eye glasses. So, what you should do is to keep your eyes wide open, on condition that your eyes are not too small. Then, get the right side of the lenses on your fingertip, this would be extremely hard, just be patient or have someone else to help you through this stage. Then, you slowly put the lenses into each one of your eyes, also , very hard. But it is not impossible!
Reading in bed is really bad for eye health. First of all, if the eyes are likened to a camera, then, as we all know, the human eye is like a camera which has the function of auto-focus. When we see the close things, such as reading a book, and the eyes need to go through a series of adjustment, so as you can see things clearly. Felling down to sleep after reading the book, it looks like that eye get the rest, but in fact, because of continuous nearly watching without rest, the ciliary muscle, the lens and the pupil need to keep sustained contraction, so in this case, it is very easy to form a spasm. Repeated long-term spasm may even lead to pseudomyopia, and cause the further development of the anteroposterior diameter of the eyeball and result in the formation of a true myopia.
Well, in my opinion, it's not a good choice for you to put in contact lenses just with your one hand. If you do it like this, it will be very dangerous that it also can hurt your eyes. Then that will be a big deal. So in your situation, I suggest you should wear glasses instead, or you can ask other person to help you. But no matter who you ask, the first thing before he/she touches your contact lenses, you should make sure they have washed their hands cleanly. Or it will make your eyes infected.