No, you should not mail a second return to the IRS at this time.
The information in the link below shows that the IRS is currently processing mailed returns received in March. You should try to contact the IRS again for some further advice using the 1-800-829-1040 phone number.
Processing status for tax forms
If your proof of mailing also contains tracking information, try to verify that the package was delivered. If you find that it was not delivered, then you should mail your return again.
@NJ_Taxpayer
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