Hello Alynis and welcome to the BC HijackThis forum. I see no signs of viruses or malware in the log. It is clean.
I also see no signs of any anti-virus programor firewall on the machine. Since there is no protection there is no defense. I would highly recommend installing an anti-virus program and a firewall to prevent any of those problems. Here is some information on free versions available for personal use:
You should definitely have a good antivirus to stop infections before they can start and spread. Here are 3 free anti-virus programs that are available for personal use (I use each of these on various machines and they are all good):
You should also have a good firewall for blocking unwanted access to and from your computer. These also are free for personal use:
It is best to have both a firewall and anti virus to protect your system and to keep them updated.