Yes, medicine can be cause of changes in urination. Check with your doctor before trying any kind of solutions as you might not understand the problem and the solution you may try might not be effective on your body.
Some medicine might cause this problem, but it is much more likely to be a result of a prostrate problem; you should go and have that checked out as soon as possible.
It is very possible that some medications could cause this. There are a lot of medications that have anticholinergic properties, which can lead to urinary retention, dry mouth and eyes and constipation.