I filed my taxes with H&R block but noticed they did not complete all forms which means I received less on my tax return can I do my amendment through turbotax??

You can amend a tax return that you prepared elsewhere using TurboTax, but it will be a real pain.  If you can go back to wherever you prepared your original return you would have an easier chore.  In order to use TurboTax you first have to purchase the desktop software and install/download it to your computer (not a mobile device).  Then you have to re-create that original return EXACTLY as it was when originally filed.  You then tell the software you are going to file by mail so the software “thinks” you filed the return.   After that, you go to the section to “Amend” the return  (It is under Other Tax Situations>Other Tax Forms>Amend a Return).  Then you amend the return to prepare a Form 1040X, which will have to be printed, signed and mailed.  Amended tax returns cannot be e-filed.

https://ttlc.intuit.com/questions/1894381-how-to-amend-change-or-correct-a-return-you-already-filed?... 

Wait about 3 weeks and you can check the status of your amended return:

https://www.irs.gov/Filing/Individuals/Amended-Returns-(Form-1040-X)/Wheres-My-Amended-Return-1

It will take about 3-4 months for the IRS to process an amended return. 

https://www.irs.gov/filing/individuals/amended-returns-form-1040-x/amended-return-frequently-asked-questions

https://turbotax.intuit.com/personal-taxes/past-years-products/

Here's another way:
You must have a copy of the original tax return you want to update.

The simplest way is to prepare your correct tax return (using TurboTax for example, or other means) and print it.

Then lay the paper printouts of both returns (correct and original) side-by-side.

You now have all the information needed to prepare Form1040X by hand.
It's pretty straight-forward.

The blank form in fillable PDF format and its instructions are available at www.irs.gov.

Mail to the same address you would mail your original tax return.