PHPMyAdmin is not a security tool, and using it is risky in itself. You log in directly using the database account, with all the privileges the account has. If your task is to update the database, this means write access. Of course you could create a limited database account that has only access to certain tables, but that's not really practical and most likely the hosting company has given you exactly one account with full privileges. If this database account gets compromised, the whole database gets compromised. It's exposed to several risks when your requirement is to be able to work on any computer with Internet access.
Having a separate tool that is limited to certain use cases is recommendable, as it can have an authentication that is totally independent from the database account, and own account for every user. The tool can also have detailed access control over who can update what, and logs for auditing the changes etc.
The cons are that creating such a tool from scratch and making it secure is not an easy task. The authentication might be bypassed, you might leave vulnerabilities for SQL injections or expose the database password with configuration mistakes. Using anything that has been developed for years, is widely used by others and gets regular security updates is preferable.
To achieve both you would look for a widely used ecommerce platform. If you really must perform administrative tasks from external non-trusted computers, it's recommended to have some multi factor authentication.