No you don't.
If you have more than one Freshdesk Account you can share you Opinyin Account API key and your question response allowance across all of them.
Simply install the Opinyin Freshdesk app from the the marketplace in each of your Freshdesk accounts and then use the same Opinyin Freshdesk Integration API key in the installation page for each.
Do not to use the same Opinyin surveys across your different Freshdesk accounts as each survey response is tagged with data unique to the ticket in the originating account. If you used the same survey across different Freshdesk accounts the agent, ticket and group IDs would attached to each survey response would not match which would cause undesirable effects in the reporting dashboard.