For a small startup, I like GrooveHQ. It’s like the Zendesk experience but less janky, much simpler, and well suited to a small team. Just have your support emails forward to Groove. Will still be email support from your user’s perspective. You can keep your current workflow going but turn on forwarding to try it out.
In my experience, any ticketing system will be a huge improvement over using a shared gmail inbox for support.
I've run my own for 15 years with no problems. So I recommend learning how to set up postfix. If you prefer not to do that, people here seem to praise fastmail pretty uniformly.
In my experience, any ticketing system will be a huge improvement over using a shared gmail inbox for support.