I've been by this place a few times, never really fished it. It's a point at the end of an island in the middle of the river I normally fish. The bottom is usually sandy and mucky in this river. The current flows right to left in the picture. Does anyone have any experience fishing places like this? I know points usually hold fish in lakes. Are rivers any different?

How big of a river ? I know   the Mississippi river   islands  have long points on the downstream side. I have fished them a couple of times for bass and didnt catch a single one , but I think the bass should be there. Especially if you can find a washed up tree. There is always a deep hole on the downstream side of trees. Always .The longer the tree has been there the deeper the hole. 

Points are good regardless of whether it's a lake or river.