Hello,
The spider in that picture is not a Brown Recluse Spider. It lacks the distinct violin shaped marking on the back, and Brown Recluse Spider legs are a solid color rather than having little striped areas on them.
The redness on your thigh doesn't have any apparent fang marks and doesn't have a target area that would be more consistent with a Brown Recluse spider bite. Keep an eye on it though to see if there is any discoloration other than a red mark.
Tom
Brown-Recluse.com