Can I apply for asylum after 3 years of my last entry?

There is a one year period from the date of your last entry into the U.S. in which you must apply for asylum. After that one year period has ended, you are no longer eligible to apply, unless there are changed circumstances. It doesn't sound like things have changed and the situation in your country is the same as when you left.

The rule is that an application for asylum must be filed within 1 year from the entry into the U.S. - unless the asylum is requested due to a substantial change in the circumstances. The change can be in personal circumstances of the applicant or in the circumstances in his/her country. An example of the first kind of changed circumstances: during the last year, the applicant publicly declared his/her homosexuality and entered into a same-sex marriage; in the applicant's country, homosexuals are persecuted and killed. An example of the second kind of changed circumstances: within the last 365 days and after the entry of the applicant, a military coup established an oppressive regime in the applicant's country; the applicant was a known activist of the party that formed the overthrown government and fears to be executed or imprisoned. Your situation does not appear to fit either category. The wars and political instability in your country have been going on for years, and you knew about it when you last entered the U.S.; so, there is no change of circumstances either within the last year or since your last entry. Moreover, despite these wars and instability, you voluntarily want back to your country after finishing your studies; this act works against your claim that you cannot return there (unless you can show that the situation became markedly worse since that time). If failure to comply with the 1-year rule disqualifies you from asylum, the court might still consider the benefit known as withholding of removal. It is even more difficult to obtain and, unlike asylum, does not open the path to a green card and, eventually, U.S. citizenship (the person in withholding is in legal limbo: he/she has to apply for employment authorization every year, and is, essentially, waiting for the situation in his/her country to become better). The benefits of this status are that the person does not have to return to his/her country and risk harm that awaits there, ability to live and work in the U.S., and, possibly, to meet and fall in love with a U.S. citizen, marry her/him, and get a green card that way (arguably, if you manage to maintain a valid non-immigrant status until the court grants you withholding, you might even be eligible for a green card through a petition by your employer). Withholding, just like asylum, requires you to prove that you have a reasonable fear for your life, liberty, and/or health and well-being in your country of citizenship as you would be likely persecuted there* because* of your race, ethnicity, religious beliefs, political position, or particular social group. When you talk to an immigration attorney about your case, make sure that you make this connection because, if it is generally unsafe to be in your country, you do not qualify for asylum or a withholding. You must show that it is unsafe *for you* to return home *because* of who you are.