Look at the link I gave you. You are basically getting the same gaming CPU. At the cost of a new board and CPU. What GPU do you have? Why not just upgrade your GPU? I know you said it feels like a CPU bottleneck, why do you say that? Double check that link again, buying the 1600 isn't really going to help you.
Edit: Here is the final page.
http://www.tomshardware.com/reviews/amd-ryzen-5-1600-cpu,5073-10.html
If you look at the chart, the 7500 and 1600 are right next to each other. With the 7500 being cheaper. Even if you OC the 1600 to 3.9GHz it's not that much faster then the 7500. You only gain ~5FPS or so. Even at $270, that's a lot of money to spend for not a lot more FPS.