At this point in time, after filing by mailing a paper tax return, you should not attempt to also e-file your tax return. Please do not attempt to do this, as that can only result in further delays or unnecessary trouble for yourself.
Instead, the best course of action now will be to wait for the IRS (and / or your state department of revenue) to begin to process your tax return. If the revenue authorities then decide that they need a physical copy of your W-2, they will send you letter (or notice) asking for you to send one.
On the other hand, it is also possible that the revenue authorities will be able to get the relevant information that they need directly from your employer's W-3 (which is the summary statement for all of the W-2s issued that year by a given employer). And in that case, if the "numbers match" the information reported on your personal tax return -- such as wages and income tax withholding and Social Security Number -- then they may not need (or ask) for your W-2 at all.
So, the smartest course of action for you (having already made this minor filing error) is to now wait and see what the government does, or what they may ask you to do. If, or when, you receive a letter asking for additional information (such as a W-2 copy), then please respond to it promptly. But it's also possible that such an additional information request may never come.
Submitting another tax (duplicate) tax return electronically, however, may only look like a fraud attempt, from the perspective of the revenue authorities' computers; and that would then create an entirely new set of problems that you would not want . . . as well as further unneeded processing delays.
Thank you for asking this important question. Please take some comfort in the fact that as long as you wait patiently, and respond promptly to any IRS (or state) communications, your tax return / refund will eventually get processed.
I followed your advice and waited for a letter from the IRS, but after almost 10 weeks nothing has come. The State contacted me, and we were able to fax our w2s to them. Nothing from the Federal tax IRS. What would you suggest I do now? Should I file an amended return? Thanks