I have opened the port to my computer's internal ip address. Do I need to open the port on the external ip too?
No, as you've already created the necessary NAT rule to establish a connection to port 3389.
However, it seems that the computer you are using at work is trying to establish a connection to a completely different port which obviously doesn't work.
By the way: The firewall rules below the first one are not necessary as you've opened your firewall to anything in the first rule.