Yes, baby is taking up more room and pushing your diaphragm up, leaving you less room there to capture the intake of air. Water does help, by the way.
Be sure they are watching you closely for preeclampsia. I had it at 36 weeks (was on bedrest from week 27 on due to preterm labor) with my son, without breathing problems, but AFTER my daughter was born, I was discharged, and found I couldn't sleep that third night due to not being able to breathe. I just couldn't catch a breath. The next day, just walking from my bedroom to the kitchen in my 1 story home made me out of breath. I thought maybe it was gas, but called the doctor who told me to get to Urgent Care or Emergency right away. I did, and good thing, because I almost passed out there. My blood pressure was skyrocketing and pulse was getting really low. I was hospitalized (without my newborn!!!) for 5 days. It was rare postpartum preeclampsia, but basically blood pressure issues.
So they need to watch that blood pressure and the protein in your urine. Also, if you get a pain on the upper right quadrant of your tummy, just under the breast, that could also be a sign of it.
While pregnant, I found going to the pool helped a LOT...the floating took the weight off of everything... as did walking. But rest when you need to, before you are worn out. And watch the stress.