River is not a Time Lord (although she's unquestionably female). She is a human with some Time Lord DNA, and the abilities (such as regeneration) that result from that. This was stated in "A Good Man Goes to War", when the Doctor and Madame Vastra discussed the DNA scans of Melody Pond (revealed at the end of the episode to be River Song). Doctor and Madame Vastra speculated that she had acquired that Time Lord DNA in the same way the Time Lords originally acquired it -- by exposure to the time vortex (in River's case, by being conceived in the TARDIS while travelling through the vortex).
Besides her biology (which has been described as "half-Time Lord", "part-Time Lord", and "human +"), even someone who's genetically purely Gallifreyan doesn't count as a Time Lord in every sense. She doesn't have the shared history, etc., that the Doctor described in the Doctor's Daughter, she's never stared into the Untempered Schism, she didn't graduate from the Academy on Gallifrey or have an Investiture ceremony, etc.
- redirectWho is Professor River Song