If I filed my taxes with H&R block and they were rejected can I resubmit them using TurboTax?

If you already paid Block, then why switch? Just fix the issue and resubmit.

Yes, you can file your return using Turbo Tax. Even though you prepared your return using H&R block, they were rejected, which means the IRS and your state do not have records of them. 

Click here to decide what version of Turbo Tax is the one you need to use: https://turbotax.intuit.com/personal-taxes/online/