Your entry clearance was cancelled and you were issued with air-side removal papers. That was for deception. What happened during your landing interview is not clear from the information you provided, but presumably some especially aggravating (and no doubt serious) factor made them decide to issue a mandatory ban right then and there.
Short of a successful appeal lodged from Nigeria, there is no way to 'rectify things'. There are success stories, you can read case histories on the Tribunal site (http://www.judiciary.gov.uk/tribunal-decisions/immigration-asylum-chamber/); but you'll quickly see that they were invariably handled by a heavy hitter in the UK Law Society (https://www.lawsociety.org.uk/).
Otherwise, and from the UK point of view, nothing will happen unless you apply for another UK visa during the ban period. At that time the ECO will have the obligation to refuse the application. There is no discretionary latitude because refusal is mandatory under Paragraph 320 (11) (iv) with aggravating circumstances.
Once the ban period is ended, you can apply again. The ECO can approve the application or refuse it on the grounds that your credibility has been exhausted. The ECO has an alternate recourse of issuing a further ban under the same paragraph. For this part, your behaviour during the original event will also come in to play.
In all events your biometrics will have been marked for long-term retention, and you won't be back in the UK for quite some time, if ever. They share biometrics with the US along with your transcript. I am not competent in US immigration, but suspect your chances of a successful application would be enhanced by having competent legal representation.
Finally, don't waste time on the internet. There's not that many people knowledgeable about Paragraph 320 and NONE of the heavy hitters surf around answering questions. :)