Yes.
You need to fix contact identity before any tool will help.
Why
Email, Instagram DM, and website chat each generate their own thread ID — no tool magically merges them unless you capture an email or phone number in every channel and use that as the join key. You didn't share volume or team size, so I'll be blunt: if you're under ~50 conversations/month, this is a habit problem; above that, it's a tooling choice. Either way, the team losing context isn't because you lack software — it's because nobody's logging "this Instagram DM is the same person as the Tuesday email."
What you actually need
- HubSpot Free CRM (free up to 1,000,000 contacts) — connects Gmail/Outlook + a website chat widget + lets you manually log Instagram DMs against a contact. Contact record shows full timeline across channels keyed on email.
- Front or Missive (~$19–25/user/mo) — if the issue is *team* visibility, a shared inbox that pulls Gmail + Instagram + website chat into one threaded view per contact beats a CRM for this exact pain.
- A habit — ask for email in every channel, every time — first reply on Instagram or web chat ends with "what's the best email to send details to?" Without that join key, no software stitches threads together.
Do this today
Sign up for HubSpot Free at hubspot.com, connect your team email inbox via Settings → Inbox → Connect a channel, then install the free HubSpot chat widget on your website. Next, in any Instagram DM thread, manually create a contact in HubSpot using their email and paste a one-line note: "Also DMs us on IG as @handle." By tonight, three test contacts have a unified timeline you can show the team Monday.
What to ignore
Skip HubSpot Service Hub Professional ($90/seat/mo), Salesforce Service Cloud, and Sprinklr — all sell "omnichannel" as a $1,000+/mo feature when your real blocker is a 5-second habit (capture email). Ignore anyone pitching Intercom or Gorgias unless you're doing 500+ conversations/month with a dedicated support team.
What doing nothing costs you
You didn't give volume or deal size, so no fake math from me. The specific compounding loss: every "didn't you already tell us this?" moment trains repeat buyers to go to a competitor who remembers them.
When to revisit this
When two teammates reply to the same person on two different channels in the same week and you find out from the customer.