If the bunny is just that, a bunny, you should give him time to adjust to eating solids. Often, when a newborn starts solids, they go through a period where they get a little constipated, it's natural.
The water however is a different matter. Do you have a bottle that he can drink out of? They don't typically like to drink from bowls, and they knock them over all the time. I would give him a day or two to adjust to his surroundings, and see if he settles in a little more, but after that you see that it's still going on, then I would take him to the vet. Hope this helps, good luck.

 70 to 100 pellets a day for a healthy rabbit  you can give him some pineapple  caned or fresh but he should also have a type of food pellets  you can get them from petco walmart  or a feed store you should call and ask what type he has been being fed its  best to stick to the same kind of food

 I was going to say, the rabbit my grandson had, went constantly. Listen to the people who have answered above me, they seem to know what they are talking about. I just know that they have a very busy digestive system among other things.

 Thanks for the advice. Winston, my bunny is doing better, I gave him some of the papaya and pineapple enzyme tablets and they seem to be helping. He is still only peeing once a day and not drinking as much as I'd like. Someone told me it could be because he is getting enough water out of the veggies and fruit? Oh and yes, I am using a water bottle which is what he was drinking out of at the shelter and I have tried a bowl too just in case. He is eating much better, but seems to be eating mostly in the night.I'm wondering if his schedule is just totally off because he is use to being in the shelter for the last 6 months. At the shelter he would hide in his home all day and then probably after everyone left was when he became most relaxed and active. Just a thought.Keep the advice coming, I'll take all I can. It's a little scary being a rabbit mom for the first time, I just don't know what is normal and what is not for a bunny!