What are your goals, aside from increasing the amount of weight you're lifting? Overall fitness, weight loss, physique? I can give better advice if I know specifically what you're working towards. In general, diet and a varied workout routine are what help offer changes to physique. So if you're repeating the same workouts every time you go to the gym, that may be why you've plateau'd and you'll need to incorporate different movements that target different muscles. If your workouts already are varied, nutrition choices are probably where you need to focus.
As far as the fitness aspect and putting up more weight, a consistent strength building program is what I would recommend. There are plenty out there to choose from. StrongLifts 5x5 is what I did to get used to the physical requirements in my current job (I went from no lifting whatsoever to getting my current job where I regularly have to move 200lbs). It is an easy program to do if you have access to a barbell. If you don't, Men's Fitness has a decent dumbbell program here:
http://www.mensfitness.com/training/build-muscle/dumbbell-workout
As far as other factors, getting consistent about your sleep like you mentioned is good. Sleep is vital to muscle recovery. Other things you could think about that are similarly in line with that:
- Are you drinking enough water?
- Is your caloric intake appropriate for your goals, and how did you calculate this?
- What is your meal plan like and are you spacing out your meals appropriately? In that line of thought, are you making smart choices about what kinds of foods to be eating when? (ie. Carbs early in the day, protein post workout, etc.)
If you're overweight or you have a higher body fat percentage, cardio would be much more impactful in terms of seeing a difference in your physique and potentially helping with the shortness of breath when you're getting over exerted. Most of the programs I've looked at that have a diet and exercise component recommend 4 days of lifting (2 upper/2 lower - spaced out) and 3 days of light cardio for people who fit that description.
Again - can give better advice with more details, but hope this helps a bit! I've dropped 40lbs and cut my body fat by 8% getting ready for bottom surgery, so I've definitely been there. Plateaus suck.