You should ask a sheila but sefira is more lenient than the 3 weeks. And also has become more lenient as time has passed (for clothes at least, as getting something new is not considered as big a deal and long ago. An example of this is that many people don't make a shehechiyanu anymore when they wear something new.) I'm not sure about a big purchase like a wig but needing it for work would be a factor to consider.