Possibly ... if you used the online program log in now and change your password and/or turn on the 2 step authentication system. 

If you used the downloaded program you had to protect your account and/or protect your files stored on that hard drive.  Seek professional assistance to learn how to do this if you don't know how.  Storing files on removable storage devices that are not left connected to your computer is best ... this leaves nothing on the hard drive to be hacked. 

Most of the time, when someone claims they got into your computer, it's a scam.

However, if you have Remote Desktop access enabled, and someone is able to remote in to your computer, they can do everything that you could do sitting in front of the screen.  That includes opening files, sending emails, and copying personal information.  However, they can't do anything that triggers a password request (like install new software) unless they know the password.

Why do you have "client information" in TurboTax? If you are using TurboTax to prepare tax returns for paying clients, you are violating the license agreement, and probably also violating IRS regulations for paid preparers. TurboTax is only for do-it-yourself consumer use and cannot be used by paid preparers. Intuit (the company that makes TurboTax) has three tax software product lines for professional preparers: ProSeries, Lacerte, and ProConnect. You can find information about all three product lines at the following link.

Intuit Professional Tax Software

You also need to educate yourself about the security requirements for paid preparers. You might want to take a professional education course on the subject. Here's a link to some information from the IRS.

Protect Your Clients; Protect Yourself: Tax Security 101