Yes, rice milk constipates. In Eastern Europe it is given to people suffering from diarhea and is usually very helpful. I find it constipating too (but I am a C, so that doesn't say much).
Rice milk doesn't cause bloating, though, at least I have never experienced that. But I'd not take it if I were you, since you are a C too. Did you try almond milk? Much better choice in my opinion.