You still owe income taxes on the money, even if your employer did not give you a 1099.

Yes.  But if you are an employee you should get a W2 not a 1099.  If you are self employed for it then they are not your employer but your client or customer.  They have to give you a 1099NEC if they paid you $600 or more for the year.  

You need to report all your income even if you don't get a 1099NEC or 1099Misc. You use your own records. You are considered self employed and have to fill out a schedule C for business income. You use your own name, address and ssn or business name and EIN if you have one. You should say you use the Cash Accounting Method and all income is At Risk.

Just enter it as Other self employment income or as Cash or General income. You don't need to get a 1099NEC or 1099K. Even if you did you can enter all your income as Cash. Only the total goes to schedule C.

How to enter income from Self Employment
https://ttlc.intuit.com/community/self-employed/help/how-do-i-report-income-from-self-employment/00/...

contact your employer. you don't want to be in a situation where it filed a tax form (w-2 or 1099)  with the government and you failed to receive a copy. this could result in misreporting and cost you $ and needless correspondence with the taxing authorities. if you are told no tax form was issued then you still need to report your income using schedule C.