It is very well possible. I do not tend to constipate EVER since I basically live of fruits and veggies and I just do not tend to constipate. Actually I "go" 3 times a day but if I ever take Ca hidden inside any multivitamin or supplement - it is "game over" O-0 !
If your constipation coincided with starting new meds and Ca at the same time, it is possible that it is Ca that is causing your constipation. Just stop taking Ca for couple of days and see what happens. If you have some improvement but not complete resolution than Ca at least is contributing but is not the only culprit. If there is not change at all than medication is the cause.

Hopefully you do realize that you cannot absorb more than 500 mg of calcium at one time. If you take more, it is just wasted. I take 500 mg three times a day and my calcium is still low, Near the minimum.

Manasul classic tea sold at Amazon.. After my surgery I suffered from chronic constipation I bought this tea on Amazon one tea bag every evening before bedtime never again suffer from constipation.