The mystery anime song was indeed Ai wa hana, kimi wa sono shushi from the Ghibli movie Only Yesterday (Omohide Poro Poro) and it is sung by the very popular japanese singer Harumi Miyako. Only Yesterday is the sixth film by critically acclaimed director Isao Takahata (Grave of the Fireflies) and was produced by Studio Ghibli (the same studio that produces Miyazaki films). Ai wa hana, kimi wa sono shushi is the ending theme song of the movie, and it is a Japanese translation of Amanda McBroom's composition The Rose, which is a pop song made famous by Bette Midler in the 1979 movie The Rose.9.5/10 I've never heard the original song, so the first time I watched Only Yesterday, I couldn't help but fall instantly in love with the song. It is one of the most touching ballads I have ever heard, and I love Harumi Miyako's mature and dramatic voice. When you're used to young J-Pop singers, it's a real change!
Here's the original music video of the song: