Hello Mary
I think that your difficulty breathing could be caused by a number of factors, but I think you're right to start by making sure your bike fits. There are several good websites that can give you a good idea as to whether your bike is the right size or not. You can also visit your lbs to get fitted.
If you have a road bike and ride with your hands on the hoods or in the drops, your back will be bent, yes, and you may experience some muscle aches in your neck as you get used to riding that way. I suppose the sensation of being bent over could make it difficult to breathe, but it really is quite natural and comfortable as you get used to it (not haviing difficulty breathing, but riding leaning forward).
As for saddle height, when the pedals are horizontal (and your feet are on them) a plumb line dropped from the bottom of your kneecap should bisect the pedal exactly. If it's too far forward, your seat is too low. Too far backward, it's too high.
I CAN sit fully upright on my bike, but only if I put my hands on the bars right close to the stem, and it's not very comfortable or aerodynamic, so I rarely do it. Yeah, and I never use the suicide levers. Use the "real" brakes."Right now I cannot ride without some weight on my arms, and I think that a proper fit would mean that I can sit fully upright. Is that true?"
Get some cycling clothes. That should help as well.
I didn't feel comfortable riding in the drops until I had been riding for several hundred miles. When you are in the drops, your back is practically level and looking up really uses those muscles in the neck!
Hope that helps a little!
Courage!
R.