Thank you for sharing your question, I think this is a great idea to ensure your customer inquires are organized and responded to in a timely and professional fashion. You would most likely need a solution that centralizes your customer service channels or a helpdesk-type app, two examples you could look into are:
Both of these app options would basically take the email that the web form connects to, and create a ticket under a centralized helpdesk system controlled by the app. Both apps are widely used and highly rated, however, Gorgias is a little pricier at $60 USD a month compared to Richpanels free plan offer (additional charges may apply).
It may not hurt to reach out to both app developers' support pages to ensure that they would meet your exact requirements. On both app listings, you should see a "get support" button, which sends your request directly to said app developers' support teams:
Alternatively, you could reach out to a local developer or Shopify Expert to see if your idea is a customization that could be developed for your shop.
I hope some of these ideas help you out moving forward, feel free to reach out to me directly if you have any additional questions, we are always happy to chat!
Hope you're having a great day!
You should check out these support ticket management apps in the Shopify app store:
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Check out the HelpCenter App. You will be able to include a contact form in your FAQ page and sync it with your helpdesk ticketing system. As with the rest of incoming inquiries, the inquiries from the contact form will have a ticket number, too.
The contact form is included in the “Essential plan” with monthly cost of $7.99 or $95.88 when billed annually.
If you require any assistance setting everything up, the app’s support team is fast and helpful!