You can get the mail tracking number of the petition package. With that we will know whether your application was mailed or not. But this year the e filling is also enabled for new H1B. So this way may not suit if your employer is filling through online.
There is no confirmation until the lottery results come out. If you are selected in lottery, a receipt number is sent with receipt notice. If not selected, a letter is sent to the employer with your name in it stating that you were not selected in lottery. So after lottery process, you can know whether your employer applied for u or not. Till then you may have to trust your employer's words. All the best for your lottery!