Here is a list of the supported processors for your gigabyte h61m s2pv
A i5-6600 is not on the list.
https://www.gigabyte.com/us/Motherboard/GA-H61M-S2PV-rev-10/support#support-cpu
The strongest upgrade would be a I7-3770K about $125 on ebay.
Your i5-2310 has 4 threads and a total passmark rating of 3628. The single thread rating is 1492
The i7-3770K has 8 threads and a rating of 6448/2108.
You can not overclock the 3770K, but the stock speeds are better than the i7-3770.
There is no such thing as "bottlenecking"
If, by that, you mean that upgrading a cpu or graphics card can
somehow lower your performance or FPS.
A better term might be limiting factor.
That is where adding more cpu or gpu becomes increasingly
less effective.
In this case, if you upgrade to a i7-3770K you WILL do better, but who knows by how much.
Here is one simple test:
Run YOUR games, but lower your resolution and eye candy.
If your FPS increases, it indicates that your cpu is strong enough to drive a better graphics configuration.
If your FPS stays the same, you are likely more cpu limited and a cpu upgrade is warranted.
Your R7-360 is a weak graphics card. You might do better updating graphics first if you play fast action games.