Well ... a few thoughts.
One is that you *might* be overdoing it. I know that when I first started out on the elliptical, I couldn't manage 30 mins at a time. I could barely manage 10 mins. Your body does need time to become accustomed to strenuous exercises.
Another is that there are all different kinds of elliptical machines and they all have different stride lengths. Some of them have adjustable strides and some of them don't - but it's why you're always advised to try a particular brand out before you buy it. You don't say how tall your brother is or how long his legs are in comparison to yours, but it's possible that this particular elliptical machine is good for him but not for you. I know there are 3 different brands of elliptical at my gym and 2 of them work really well for me, but one of them causes my toes to become numb and my legs to hurt within 10 minutes of being on it. I've come to the conclusion that it's just the *wrong* machine for me to be using. (I am 5'4" and have pretty short legs, so I'm not surprised by this.)
Aside from that, my final thought is that even though you don't have a history of knee or joint problems, you are significantly overweight and starting a new form of exercise, so it's entirely possible that the pain you feel is damage to your knees from beginning this form of exercise.
I think the best advice I ever got from anyone about exercise is that discomfort is ok, soreness is ok, but if you start to feel pain ... stop doing what you're doing.
Maybe you should wait on using the elliptical - or at least THIS elliptical - until you're a little more used to exercise or have lost a little bit of weight through other means.