Can you claim healthcare workers bonus employer said I received but I did not

If you did not actually receive the bonus, then no, you should not claim it as income.  However, if they reported it on a 1099 then you will need to add it and then make a correction to the income to remove it.  Be 100% sure that you did not receive this before you remove this from taxable income. 

To enter the 1099  as non-self-employment income take the following steps:

• Income
• 1099-MIsc under Other Common Income
• Enter the information from the 1099-MIsc
• Continue through and say the work does NOT involve work that is like your main job
• Select the years you received it
• Say no, to did this involve an intent to earn money

Then you will take the following steps to remove the income:

• Income
• Less Common Income
• Miscellaneous Income
• Other Reportable Income
• Answer Yes to Any Other Taxable Income
• Enter the description such as 1099-Misc received for bonus that was not received or paid
• Enter the amount on the 1099-Misc as a negative number. 

If it was reported on your W-2, then you will need to ask for a corrected W-2 from your employer.  If they actually did pay it, then they would have documentation of that.  If they did not pay it and refuse to make a correction, you can  file form 4582 as a substitute W-2 by following the instructions in the link.