This is a very common problem. What you need to do is make sure that your local machine name, its domain name and all of its aliases are in class w. This is how sendmail knows who (e.g. which domains and hosts) it is supposed to accept mail for. Make sure you have this entry in your macro configuration file:
In /etc/sendmail.cw add your domain name, your machine name and all of its aliases, each on a line by themselves. Finally, restart sendmail and you're done.