Can people own creeks in Ohio?

I live out in a pretty rural area of Ohio. Naturally, I like spending a lot of time outdoors, and one of my hobbies happens to be fishing. My house is about two miles down the road from the spillway to Cowan lake, which is where i go fishing. All the water from the spillway flows into a creek, which flows right past my road. After i'm done fishing, I usually just walk through the creek until i get back to my road. I've been doing this for years & never had any problems. Recently, on my way back, a man who lives across the street from the creek came down while i was walking through it & told me to leave because i was on his property. I wasn't walking along the shore, I was actually in the creek. I'm wondering, can you actually own a creek in Ohio, or is it state property since it comes directly out of the spillway?