OP stated it happens to their "best" shirt, so those are $25 upwards easily. Take two, get one wool.
I suppose washing intervals depend on work, climate and personal disposition but in any case you get way more mileage between washes on wool than cotton. My cotton shirts would last only two days before I had to wash them again and they were never as fresh as wool shirts straiht from the washing machine. I also did not say "wear it for two weeks in a row" but one 2-3 days ,then hang it oit in the fresh air while wearing the next. Then after some days you can wear the first again because wool is kind of self cleaning and anti bacterial. No problem. I have daily meetings in person and I have to be clean and nice.