You actually can file an amended return for 2014. If the amended return shows a refund you will not get the refund, because it's past the deadline. But if it shows additional tax due, you have to pay the tax.
Amending to change from Form 1040NR to Form 1040 is a bit complicated. The instructions for Form 1040X tell you what you have to do. (Form 1040X is an amended return.) If you were dual-status in 2014, which seems to be the case, it's considerably more complicated, and you should probably get professional help.
The question is whether it's necessary or advisable to amend your 2014 tax return because you are applying for citizenship. That's an immigration question, not a tax question. I can't advise you about that. You should consult someone who is familiar with the rules and procedures for naturalization, perhaps an immigration lawyer. My impression, from looking at the naturalization information on the USCIS web site, is that they probably are not going to look at your 2014 tax return, so amending it might be a waste of time. On the other hand, your answer to question 8 in Part 12 of Form N-400 should technically be Yes, which would require you to provide an explanation. But I'm not knowledgeable about these matters. I have no idea why they ask that question or what they do with the information. That's why I think you should consult an immigration expert.
If you do file an amended return for 2014, keep in mind that it typically takes the IRS 16 weeks to process an amended return. Yours might even take a bit longer, since it's an unusual and complicated situation.
