I want the whole Eevee evolution set (who doesn't!) so I need a female Eevee but the woman gave me a male one...can I get a female one anywhere else (without trading)? Or do I have to find a Ditto?
You would have to find a Ditto, or find another Eevee. They can both be found in the Trophy garden south of Hearthome city after you get the national Pokedex.
Source: Personal Experience
For more information on the Trophy garden click here.