I found out that the water I used to dissolve my DNA after phenol-chloroform extraction was contaminated with bacteria (not sure which, but likely E.coli used for cloning). Can I remove these bacteria by simply performing another round of phenol-chloroform extraction on this sample? Thanks!
Hmmm, probably not. The bacteria will likely be killed by another extraction but if any bacterial cells were lysed then you'll get bacterial DNA in your sample. That may or may not be an issue for your planned next steps. Still, it's not ideal.
I would vote to get nice fresh sterile water (you can aliquot and freeze it) and re-do your DNA extractions.
You could remove the bacteria by filter sterilization but would still likely have bacterial DNA showing up in any PCRs or sequencing. If your samples are not precious I would suggest doing another fresh extraction.