Reporting Unemployment in 2 states?

So, to preface, I lived in Oregon until September of this year, when I moved to New York. I was laid off in March and began collecting unemployment benefits from Oregon (No taxes, state or federal, withheld). When I moved I was told that I was still eligible and should continue collecting unemployment from Oregon while living in New York, which I have done since. 

 

My question, then, is on which state I should be paying the taxes on my unemployment to. My inclination was that since the money was coming from Oregon, I would just pay Oregon income tax on my benefits for the entire year. But I am wondering if I need to report my unemployment from Oregon as taxable income in New York after my move. If so, do I have to manually calculate the amount I received in each state and report it that way? Does that then mean that I'll be "double taxed" by both Oregon and NY for unemployment received after my move?

 

Sorry if this is confusing, I am clearly struggling to understand what to do myself! Thank you.