YES YES YES, I certainly had the same exact problem when my now 6yr. old went off of breastfeeding to formula.
I breast fed until she was 5 months old. Up to that point she was anything but constipated.
They did run all kinds of tests to figure out if there was any other cause for it, because there can be nerve damage around the tailbone area. I went to a specialist at the DAyton Children's hospital for this testing. It seems extreme but even at age 12 months she was still constipated a lot.
At least it ruled out anything else being the cause.
The very first couple weeks I switched her to formula, she went 4 days and had not had a bowel movement. I tried Karo syrup, sugar in water, etc.... everything that people told me and nothing worked. Someone finally suggested apple juice. That did the trick and it worked on the second little bottle of that and of course, then she had a major blow out. In the next few months, when she would get constipated I would use the apple juice and that would do the trick.
AS she got older, it no longer worked!!! Now, it takes dynamite to work on her.
It is ok to use Milk of Magnesia. It is mild and you can use more than what they tell you to.
My daughter often only has a bowel movement everyother day. I am the same way (in fact for me, it is sometimes every 2-3 days) so she is just taking after me. Yes sometimes it is hard and discomforting but that is just the way it is.
If you can get your baby to take jarred prunes that can work great too, just go with the smallest jar to find out. My daughter who is only 20 months is very sensitive to prunes and it goes right through her, but not the 6 yr. old.
Just hit the vegetables (broccoli is the all around best) and WATER (not milk or juices or other drinks). My biggest problem is I don't drink near enough water. Water is the only true purifier and cleanser for your body.
I would suggest asking your dr. about a specialist on the constipation issue. It never hurts to do the tests just for peace of mind!!!!!!