I saw screenshots of what I believe to be a full chapter of the story online between six months and two years ago (2017) on Tumblr. The original post was the mangacaps in a photoset with the images continuing into the caption and no source given at the bottom, though after someone asking "what is this called?" someone replied with the title and said something like "please read it, it's so funny."
A summary of what I saw: a little girl with her mother in a hospital room, watching a TV show about a magical idol girl with the power to help others. Her magical familiars, or maybe her enemies, may have been vegetables...? I think they looked a little angry. She tells her mother that she will become like the cartoon character and do magic to cure her illness, who then laughs and pats her head in encouragement.
Later when walking with a friend, they find that cartoon character's wand with someone else's trash on the side of the road. They debate on if it's okay to take it and who should have it, and ultimately the protagonist gets to keep it! She shouts that she's transformed into the magical girl character and immediately after begins to hear birds on a telephone line talking to her, proving the wand is real?!?! The birds tell her she's too young to do magic, but if she was older, like the pretty teenagers passing by, then she could. So she transforms herself into a high school girl!!!!!!
Flash forward to her standing up at her desk in a classroom with other teenagers sitting behind her, proclaiming with a straight face "and that's why I can't solve the problem on the board."
The little girl is originally an elementary schooler, somewhere from seven to ten years old, with black hair and dark eyes. Maybe she wore pigtails, maybe a hair clip..? As a teenager her hair is long and straight, I think in a hime-cut hairstyle. Her high school uniform is a blazer rather than seifuku. Maybe her name was Ai or Haru, something generic like that but I have no idea, and I think the cartoon magical girl on TV has a name with P in it. Puri puri something, perhaps.
All of the characters appear to be typical Japanese people. I don't know where in Japan the story takes place, but the high school class appears to be fully populated and in an ordinary school, and when the two little girls find the wand, they are walking in what looks like a suburb with high fences shielding the houses from the road. All signs point to the time period as modern day.
I've already looked on anime-planet, mangaupdates, tvtropes, and myanimelist, looking for stories with age transformation/age progression, sick parents, curing sick mothers, magical girls, finding something by accident, and wishes. All with no luck, but maybe I am just not using the right filters/terms.
I imagine it was an English scanlation rather than an official release, the original language being Japanese. Based on the fairly modern art style, which includes no crazy hair, ahoge or unreasonably sized eyes, I estimate it was drawn at least after 2014. It is in black and white and not 4-koma. I have a feeling the magical girl theme is not the main plotline and it is a comedy, slice of life/school life story, but I can't say for sure.
This manga seems so funny, I really would like to read it. Please help me find it!!! Thank you so much.