I realize this is an old post, and I hope you get it and it helps. I am not sure about the Beaver Creek around Jackson, but I am aware of the Beaver Creek in the Northeast corner of East Feliciana Parish. Beaver Creek is located just north of Felixville and Hwy 432. Beaver Creek ties into the Amite at the Northeast portion of the parish. Beaver Creek Rd. also crosses Beaver Creek. I am also researching the Whites in East Feliciana, they are my relatives. The only problem I have encountered is that according to the Clerk of Court's office in Clinton, there were 3 families of White's that all migrated to East Feliciana around the same time from mostly Darlington County, South Carolina. In the 1820 Federal Census of Feliciana, Beaver Creek, there are 2 White's listed as head of households: 1)John White who had 10 males & 4 females living in his household 2)Joseph White who had 5 males & 4 females living in his household and also lived next door to John.
I live in Clinton. I have purchased a Parish map from the Police Jury, which has helped greatly with research. It shows roads, creeks, and the property boundaries from the original 1828 Land Survey by the GLO. If you live in Baton Rouge, you can purchase them at Baton Rouge Blueprint on Goodwood. My ancestors that I'm still searching for more info on are Green B.(Berry) White and William & Margaret Campbell.
According to the Land Survey records, There is a John White that owned land in section #88, this section is located south of Hwy 432. Joseph White owned land in section #64 which is north of Hwy 422 on the MS. border at the end of Dalton Dunn Lane. These "sections" can still be seen in the background of current topographic quad maps, these are usu. the reddish brown numbers in the background of the map. you can also see the majority of the original property lines represented by broken red lines.
I know this is a lengthy reply, but I hope it helps.
Brad J. DeFranceschi