Wish ppl would learn to actually think about their suggestions before opening their mouths.
You have only one viable option for upgrade, anything lesser will just leave you wanting. That's the above mentioned i7-7700k. That's the biggest, baddest, meanest, strongest, fastest cpu available for your current motherboard. No 8 or 9 series will work, ignore all those other suggestions. There's 6th/7th lga1151 v1, and 8th/9th lga1151 v2. They are not the same regardless of pin count, and not compatible.
Fps limits are all cpu. It pre-renders every frame sent to the gpu. Gpu just has to live upto the limit, or fail, depending on detail settings and resolution. Your current cpu is capable of @ 300ish fps in csgo/office map. That 300fps gets...