A person who had my phone number before me has an account. I'm worried if someone attempts to use that phone number they will gain access to my account as well.

No.  Establishing an account requires more than a phone number.  The phone number is usually used to verify access.  

To access your online tax returns only someone who has the User ID and Password for the account can access the returns, not just a phone number.

You can change your TurboTax account information at any time.

See this TurboTax support FAQ for updating your account information - https://ttlc.intuit.com/turbotax-support/en-us/help-article/account-status/update-turbotax-account-information/L0YoC0H31_US_en_US?uid=lv16srr4