Can I e-file my return now, because the IRS still hasn't received my printed return?

Sorry but I have to ask.  It's  common problem.....did you also mail a state return?  Did state get theirs?  Did you send federal in the same envelope with state?  Some people have been doing that.  Federal and state go in separate envelopes to different places.

When did you mail it?  It takes at least 4 weeks for a mailed return to show up on the IRS Refund lookup.  Did you call the IRS and ask them?

Did you mail with tracking service to verify that the IRS received it?

Are you getting a refund of did you owe?

What does the IRS website say?

You can check the IRS Where's My Refund website:
https://www.irs.gov/Refunds

If you e-file AND the IRS receives a paper return then both will get flagged for review which can delay everything for many months.