Can I find out if I forgot to add state tax deducted on one of my incomes?

Best thing to do it is to go through your return again in the program line by line and see what information was reported. If you find that your return is completed and accurate, there is nothing else you need to do since you already filed your return. 

If you find that there are errors on your return, you are able to file an amended return to correct those errors and send it in. You should not try to amend your return until the original return it has been fully processed and you have received your refund or your payment has cleared.

Amended returns do not “catch up” to your original return and replace them; they are processed as two separate returns.  Amended returns have to be printed and filed by mail.  It can take the IRS up to 12 weeks or longer to process them.   If you are due a larger refund than on your original return, your amended return should only show the difference and you will receive a separate check for it.  If you owe money on your amended return, it will show only the new amount owed, you will have to mail a check with the return. You can check the status of your amended return by clicking here: https://www.irs.gov/filing/individuals/amended-returns-form-1040-x-/wheres-my-amended-return-1