There are two free options you can try:
VLC offers a more friendly GUI interface though (IMO) it's much more limited. ffmpeg is much more powerful, but it requires you to be command line savvy.
Personally, I prefer ffmpg. They have a tutorial on how to stream point-to-point, which is what you are looking to do
Point to point streaming
If you want to stream "from one computer to another", you could start
up a server on one, and then stream from FFmpeg to that server, then
have the client connect to that server (server could either be on
client or server side computers). Or you could do a point to point
type stream, like:
ffmpeg -i INPUT -acodec libmp3lame -ar 11025 --f rtp rtp://host:port
where host is the receiving IP. Then receive the stream using VLC or
ffmpeg from that port (since rtp uses UDP, the receiver can start up
any time).
or
ffmpeg -i INPUT -f mpegts udp://host:port