I can't help you very much but yes Lindsay is in Garvin County.I have a copy of a booklet printed for the Golden Jubilee of Lindsay and in it is a picture of the Lindsay Hospital as it was in the early 1950's.It lists Dr. E.B.Pool and Dr. W.E. Pool and Dr. Mildred Pool also R.M. Pool R.N.
Farther back in the booklet Dr. W.E. Pool is listed as the health officer for the Health Dept.
Hope this is of some help to you.Another good place to check is the Garvin County site on the Usgenweb. Good luck Sonya Smith(born in Lindsay, live in California)