amritsari,
Sorry, it is now past the e-file cutoff date for 2021. The cutoff was back in November 2022. See the IRS website https://www.irs.gov/faqs/electronic-filing-e-file/due-dates-extension-dates-for-e-file/due-dates-ext... for details.
When you paper file, I recommend you send it with a service that gives you a tracking number to let you know when it was delivered. This sets a cutoff date for the accumulation of any penalties and interest should the return show you owed money on your return(s). For the US Postal Service, the green Certified Mail slip is all you need for that, and don't spend extra to get a return postcard for proof of delivery. The IRS website https://www.irs.gov/filing/private-delivery-services-pds gives the options for private delivery services such as FedEx. Use the same process for your state income tax return if you live in a state that imposes an income tax.
Finally, yes, it will take some time, perhaps several months, for that return to be processed by the IRS. They are hiring new staff to deal with the backlog of approximately 1 million paper returns. I, myself, am old fashioned and found the delays were on the order of 6 months during COVID times.
