As Frank said it isn't a good idea to connect to the internet without a firewall, I will take it a little further, it is like playing Russian roulette with an automatic, without protection the time to getting infected is counted in minutes not hours. A firewall is an absolutely essential part of your system security, without it you will fight an uphill and probably a loosing battle to get your system clean.
Any malware that manages to get past your defences will have free reign to connect to the internet to either download more of the same, pass your personal data (sensitive or otherwise, user names, passwords, keylogger retrieved data, etc.) or open a backdoor to your computer, so outbound protection is essential. Install the firewall now.