How would I double check to see if I entered and filed my 1098-E student loan interest for the past 3 years? Can I claim/file the loan interest for the past 3 years?

For 2019, the student loan interest deduction is reported on Form 1040 Schedule 1 line 20.

For 2018, it was Form 1040 Schedule 1 line 33.

For 2017 and 2016, it was Form 1040 line 33.

First, check your actual Form 1040s from the prior year to see if anything was reported.  If not, you may have been affected by a phase-out for claiming the student loan interest deduction.  You will need to check your Adjusted Gross Income (AGI) for each year to determine if the phase-out applied to your return.  

The phase-out for 2019, 2018, and 2017 for AGI (without regard to the student loan interest deduction) greater than $85,000 or $170,000 for Married Filing Joint.  If you use Married Filing Separate, then no deduction is allowed.

The phase-out for 2016 was AGI greater than $80,000 or $160.000 for Married Filing Joint.

If you find that you did not claim the student loan interest deduction and you would not be impacted by the phase-out, then you can amend the prior year returns in order to claim it.  The deadline to amend 2016 will be April 15, 2020.