No, she's a human who was "genetically altered" by the time vortex because she was conceived inside the TARDIS, giving her some of the characterists of a Time Lord, such as regeneration. She didn't inherit them, she acquired them in the same way the Time Lords originally acquired them.
The conversation between the Doctor and Vastra (the Silurian) made the specific point that River's acquisition of Time Lord characteristics was not just because she was conceived inside the TARDIS. It was because she was conceived inside the TARDIS while the TARDIS was actually travelling through the spacetime vortex. The strong implication of that conversation was that it was the vortex that was important and, had the TARDIS been stationary at the time of conception, it would have had no effect on the child.
The Silence may have also modified her in some way to make her closer to a Time Lord, to use as a weapon against the Doctor.