there is a number of variables here. age, are you or where u a smoker, the burning is not normal this would indicate some sort of issue with the alveolis, the air sacks in your lungs or maybe even copd the fact that it lasts for hours is the concern, feeling out of breath for 5-10 minutes is normal. breathing through your mouth is not a concern but u should breath in through your nose out your mouth, getting back in shape is great but depending on your age and how out of shape you were their may already be damage to your lungs. do you cough when your out of breath and do you cough up fluid if so that would indicate, copd - pnemonia you may even have nodules on your lobes all of this can be verified through cat scan. my concern is how long the burning is lasting. please see your doctor. im only a paramedic but this is my opinion
I'm 25 male, and I only smoke maybe a few times a year. I don't have any medical issues like COPD. I've read that having a slight burning sensation is normal for beginners. I'm also a little bit overweight so that has an effect on my lungs/heart etc.
Most of my time has been used for self-study aerodynamics and jet propulsion, so I wasn't getting that much exercise until I started running.