Constipation is not uncommon, particularly when you've made a change to your diet.
The three easiest places to start are, one...drinking more water. This is how we enable affective flow of waste products along the gastrointestinal tract which speeds up digestion, so it's really important.
The second thing that can cause issues is brown rice, because it's a little harder to digest for some people. For some, simply changing to white rice is enough, or perhaps substituting it for something else all together is the way to go.
The third thing is dairy. Once again if this is a new addition to your diet, it may be causing issues for you. Obviously calcium is incredibly important for us, but perhaps a reduction in dairy may help.
Prunes and Metamucil may also help.
Perhaps keep a note or diary of what you've changed and what results you've seen, so you have a sense of what is and isn't working.
Always talk to your doctor if you have any concerns.