Question

Looking for Ethel Rimmer who moved to US and born abt. 1888

Answer 1

You didn't give much info as to where she was born, or if she married (spouses name)/had children etc and where in the US - so it's hard to determine which Ethel Rimmer she might be.  Here is a possibility.

https://familysearch.org/pal:/MM9.1.1/M91R-31M

1900 census

Name:                                               Ethel Rimmer

Residence:                                        Marshall township, Calhoun, Michigan

Birth Date:                                        Apr 1888

Birthplace:                                        England

Immigration Year:                            1889

Enumeration District:                       0055

Page:                                                 8

Sheet Letter:                                     A

Family Number:                                180

Reference Number:                          50

Film Number:                                   1240705

Image Number:                                 00507

Household                                        Gender/Age/Birthplace

Self Edward Rimmer                       M/ENG                                                 

Wife Hellen Rimmer                        F/ENG                                                  

Daughter Ethel Rimmer                   F/ENG                                                  

Daughter Eva Rimmer                      F/ENG                                                  

Son Wilfred Rimmer                        M/MI                                                    

Daughter Gillitta Rimmer                 F/MI                                                      

Daughter Bernadine Rimmer           F/MI                                                      

Daughter Luella Rimmer                  F/MI                                                      

Son Walter H Rimmer            M/MI

Answer 2

Here's an alternative answer from my family tree which is not yet complete on WikiTree - my grandfather, Frederick Rimmer 1881-1951, had a sister Ethel who was born in 1892 in Southport, England. She came to the US in 1911 with her mother, Sarah Gaff, and two sisters: Emmie and Maude. However, a month later she returned to England with her mother and Maude. Sarah and Maude returned to the US in 1915 but apparently Ethel stayed in England and I have not researched her further at this time.