Its likely becuase you have mirc set to the default DCC ports 1024-5000
Tools/options in the options menu open CONNECT and select OPTIONS, click Advanced, and change the FIRST and LAST DCC ports to something else like 4000-4010 or 6123-6132 or what ever ya like, just stay away from anything you know u already use. (you wont really need more than a range of 10 in there at the best of times)
If this allone doesnt fix it, (which i think it well), then you need to also clear those ports for inbound connections to your pc in nortons.
The reason you are getting the attack message, is becuase when you send a file, you tell the reciever your IP and a Port number, and instrcut his irc client to connect to you using that IP and Port, once connected you then send him the file using that connection. Nortons however knows nothing of this, and just sees some random person trying to connect to your PC, there are a pile of viruses/trojens using port 1024, so mirc also using it is the likely mistaken attack message cause.