You're running both windows & linux? Hmm...
Haven't used windows since XP days but here's what you can do on Linux.
1) Check all network connections, services that are listening or running. Turn off unused services, etc.
watch -n5 netstat -naultp
lsof -i
watch -n5 ss -al
2) Check if any of your interfaces is running in promiscuous mode (this is done if something is sniffing the network from your computer - like a backdoor or something running in your computer)
ifconfig -a | grep -i PROMISC
3) Analysing traffic using Wireshark as usual is quite important, your system utilities might be backdoored, but that won't stop wireshark from capturing and displaying network activities to and from your computer.
4) If your computer is used by more than one user you might run this to check out who is using what, etc. or who logging remotely from what IP, etc.
w -s -i -f
last
Keep in mind that all these commands need to be run as root, or root privilege otherwise it's useless. Also never install any binaries or programs outside of your distros repository unless you know what you're doing.