Linux (Debian) Pro! Need To Check My Server For Possible Limits/Issues

I use my linux server as a proxy server with many tcp connections at around 4k connections. Using a python script with screen. But it seems it doesn't work right and always work fine when I use new screen (Many screens vs 1 with all connections). I would like for someone to check my server (I have increased ulimit limits + added ipv4 tcp tunning and also there is no error at syslog) But it seems something isn't right. I need full check to understand what do I do is my server is maxed out or it has some issues that can be fixed but I'm not aware? Thanks! Looking to pay around $20 for this. It's simple 1 script and clean server should be quick for someone who knows what he does!