Have a Trad IRA but thought it was a Roth, messed up some tax years. How do I fix this?

Hi there, thank you in advance for any help. 

I have a traditional IRA but I just realized in some years I treated it as a Roth IRA on my tax return and then on other years I treated it as a Traditional IRA. I would like to fix this so that all of the funds in it are legit. I think the best way forward would be for me to pay back taxes maybe, then convert it into a Roth. Here's what I did:

On my return for year 2011: I put in $1200 of contributions and counted them (incorrectly) as ROTH. So no deduction taken. 

On my return for year 2012: I put in $5000 of contributions and counted them (incorrectly) as ROTH. So no deduction taken. 

On my return for year 2013: contributed $5500 and correctly counted as traditional, so I took the deduction. 

On my return for year 2014: Same. I contributed $5500 and correctly counted as traditional, so I took the deduction. 

Now I want to clean this mess up. I would prefer to somehow pay the back taxes maybe so that I can convert it to a Roth. What's the best way to do this? Can it be done? Did it happen too long ago? What are my options? 

Thank you again