Thanks for the suggestions.
I can't build a completely new system, because I can't afford it. When building this one, the focus was on getting something cheap that can run games and upgrade in the future (Originally it had only 4GB of RAM and no dedicated GPU).
I don't think I'll be getting that ASUS strix B350-F, because of it's price. The price of this MB, plus 16GB of DDR4 RAM plus the CPU is 2150zł, enough to get me a GTX 1070.
I can get some used parts (MSI B350m Mortar, G Skill Trident Z 8GB 3000MHz) and a new Ryzem 5 1600 for around 1500zł, enough to get me a GTX 1060 6GB.
EDIT: Here is how it would look like: PCPartPicker. I already have the HDD, SSD, PSU and Case.
And this is how it would look like if I were to replace the GPU: PCPartPicker
Is my CPU really that big of a bottleneck? I thought it's 4 cores at 4.4GHz were enough and my old HD7850 was holding me back.