Cruiser,

You may be thinking of the Wallflower rhyme.

In "Play Songs of The Deep South" Altona Trent Johns, 1944
tthere's a version called "Water-Flower" The first verse is completely different:

1st verse: Water-flower, water-flower
          growing up so tall
          All the young ladies must surely, surely die
          All except 'Lindy Watkins,
          She is everywhere=
          The white folks say, the white folks say,
          Turn your back and tell your beau's name.

end of quote--
But the second verse of that song has the verse you quoted:

2nd verse Doctor, doctor, can you tell
          What will make poor 'Lindy well?
          She is sick and 'bout to die
          That will make poor Johnnie cry.

end of quote

As you can see that's the same as yours except for the change in names. Now if your name is Ronnie and your sister's name is Nancy that would account for the name changes...

"Water-Flower" has a different ending than the one you gave:

3rd verse Marry marry, marry quick!
          'Lindy, you are just love sick!

4th verse Johnnie is a ver' nice man,
          Comes to the door with hat in hand,
          Pulls off his gloves and shows his rings,
          "Morrow is the wedding-day.
---
"Water-flower" is described as a pantomine ring {cicle} game with one girl in the middle; a boy is said to act out the role of the doctor {This was before Women's Lib} and the doctor selects the boy whose name 'Lindy had mentioned to come into the center of the ring and act out the role of "Johnnie".
---

This is the first time I've seen or heard your "a bottle of ink to make him stink/a bottle of wine to make him shine" verse.

I remember this teasing rhyme from my chikdhood {1950s)
Ink a bottle of ink.
somebody let out an awful stink.
It was Y-O-U!

end of verse

That may have been because someone really had "let out wind", but not always. "Ink Stink" was also used as a counting out rhyme. According to my daughter who is a second grade teacher, the verse is still being used both ways.
--

There are A LOT of other children's rhymes with the "Momma Moma I feel sick" verses. The oldest one I found was 'Old Aunt Dinah sick in bed/called the doctor and the doctor said/get up Dinah, you aint sick/all you need is a hickory stick! {source either Scarborough "On The Trail Of Negro Folk Rhymes" 1927, or Talley "Negro Folk Rhymes", 1922.

Also I know there was at least one other thread where the Wallflower rhyme is discussed. Perhaps someone will put up that link..






thfrom The South that tdthe old book from te
I believe you are ttalkin There are also a lot of "ink stink a bottle of ink" children's rhymes also.