Outgoing Outlook email failure

My desktop PC (Dell) connection is an AT&T hotspot. We use gmail.com addresses and a work domain but I work within Outlook. Suddenly outgoing emails are bouncing back. Called Avast security people who say my Ports are blocked & I must call At&t to fix. At&t said they don't have access to Ports so can't fix it. Avast has removed/saved my gmail accounts as they tried to fix the problem. I've tried the help pages "Problems Sending Mail-Receiving is fine" and "How to Set Up your Email in Outlook 2010" but clicking on the existing gmail account. I tried POP3 and IMAP settings...so far everything has failed. I tried switching from 25 to 465. Avast said they can't fix the remainder of my issues until this Port problem is fixed.