Mekira
A few years back I totally revamped my crawl stroke and changed how I was breathing.
The first thing that needs to be done is get your correct body position. If you are patient and willing to do it the best way is to invest in a swimmers snorkel and zoomer fins. Then do lap after lap of drills where you simply maintain the proper head and torso position. Let me know if you are interested and I will describe how to do them. The fins help w/ momentum and keep your legs floating a bit better and the snorkel helps so you aren't worrying about needing to breathe.
Once you have the proper head postion and body roll down when you remove the snorkel the breathing is automatic and you can easily do it from either side.
It is not something learned in a week (I did drills only 3x per week for 3 months) but I highly recommend it in the long run because your stroke will be much more efficient and you will be able to do the distance much easier.
I went from doing a 1700 yd varied workout in an hour wearing long fins and a snorkel to doing 2300 -2500 yds in an hour w/ no added equipment
It's about the journey and being in the moment, not about the destination