What email client are you using? If you have an email account w/ your school, what's the SMTP settings for it (mail.your.domain i.e. mail.tu.edu is usually a safe bet.. I don't know Texas colleges' domain names, sorry.? I can explain it better with this information.
Basically, I see this setup. You're using Outlook, Outlook Express, Eudora, whatever.. right? And you have two accounts. You have your Cox account (which uses the cox POP3 server to receive mail) and your school account (which uses the school mail server to receive mail). You modify your Cox account so that it still receives mail through the POP3 server, but it now sends mail through your schools SMTP server (not the Cox SMTP server you probably have it set to now). This will allow you to send mail from your Cox account (using you Cox email address). It just is going through another server, which is fine. Since you're on your school's network, they should allow you to send email... no matter what the address is (blahblah@cox.com).
Think of it this way.. you own two houses.. now usually.. you walk outside and talk to people out of one house. But for some reason you decide to go to the second house... you walk outside and talk to the same people the same way out of that house.. it's just a different house. They don't notice a difference, and once you make the switch, you don't either (unless you go home, then it's back to the "original house" for you).
I'm fairly drunk, so that example may not make sense, but the explentation does (I re-read it). If you set the SMTP server for your Cox account to send through the SMTP server for the school you're at.. you should be able to use your Cox account no worries. The SMTP server you use does not add/change the information of what your email address is.. so if it's set up to send from the blahblah@cox account.. it'll do that.. no matter what server it goes through.
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Side note about Spammers:
If ISP's left their SMTP server open to computers that weren't on their network (like the above case where someone from another domain is trying to send email, even though they're a legal user) spammers could use and abuse them. Anyone could send an email through that server with a fake username and address.. and they could send hundreds/thousands/millions of emails from that server, getting that server into trouble. "Why doesn't the SMTP server just validate that the username in the email is a valid account?" you ask? Because the spammer could easily set their email address to be
soandso@domain.com and send the spams without any problem. SMTP does not require a password for a username, so it isn't possible to use the mail username's as a verification feature. You must use the IP, ensuring the user is on your network. Sure someone who is using you as an IP can spam people.. but at least you have record of who they are (they had to register to become a user, right?) and can take the correct action.
There IS secure SMTP, where you use your normal username and password to send mail. I imagine that this would do away with the "have to be on the network" restriction, but I've never tried it. I don't know for sure. Just a guess.
Once again, I'm fairly pissed as I write this. Your mileage may vary.
Hope this helps, let me know if you need more help.