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That's incorrect. As usual, there are excellent, free, open-source solutions like http://osticket.com
Hiring a programmer to reinvent the wheel on an incredibly common task like a support ticket system would not be wise.
4 months, 4 weeks ago on In the Trenches: Team vs. Individual Customer Service
Even if the team concept is best, it seems you're not using the right tool for the job. A HelpDesk-style tool where a customer opens a ticket and then can simply reply to the emails is the correct tool. Your team works in a tree-based online interface that keeps all a customer's correspondence in one place, has an easy interface to view all unanswered responses, keeps all replies in one central thread per issue, etc. Easier for customer, way easier for you.