If I wrote my own name on the ballot while voting for the president, don't I also have to concede to the winning candidate on Election Day, like the other candidates do? Is there a rule that only requires a concession from the top 2 candidates?
Concession in the US presidential election is a political courtesy, not a constitutional obligation.
It is common practice in the United States for the losing candidate to concede as soon as the election results from the states are published and their defeat becomes obvious. Note that at that point they technically didn't lose the election yet, because the electoral college did not vote yet and congress didn't certify their results. The reason for the official concession is that it signals that the losing candidate will no longer stand in a way of an orderly transition of power to the new administration / an orderly transition to business as usual for the incumbent administration.
For example, in 2020, the incumbent president Donald Trump did not concede after the votes in the states were counted, because he hoped to overturn the election either through legal challenges in individual states or through a procedural loophole during the certification of the election results in Congress. As predicted by most legal scholars, those endeavors proved to be futile. But not only did this cause a delay in the process of transfer of power to the newly elected Biden administration. Trump's refusal to concede was also considered the catalyst for the 2021 storming of the US Capitol.
But when you were not a serious contender for the presidency in the first place, then nobody was holding their breath for you during the transition period, and you are unlikely to mobilize a mob which would be any serious threat to any political process. So your concession would not be required. (But if you do have followers who might be fanatic enough to commit violence in your name, then it would be nice of you to tell them that you concede anyway, so they don't do anything stupid).
In the United States, it really depends if you had enough votes to carry a state, unlike say, a local, county, or even state election, the President is elected through an indirect, Electoral College.
Basically, people vote, and electors of each party decide, based on amount of votes, a particular party gets that state.
In terms of concession, it really only matters if you "won" that state or not, as such, it is nearly impossible to "write yourself in" to the Presidency of the United States.