Take a look at the sentence again:
For a sentence to be a comma splice, you must have two complete sentences joined with a comma. In the example above, no such comma exists. Rachel painstakingly ironed her linen shirt is one sentence. All the while, she was thinking … begins the second sentence. Because only empty space exists between the two, you should call this error a fused sentence.
Remember that both comma splices and fused sentences are major errors. They make your reader think that you cannot write a correct sentence. Because the sentence is the most basic building block of a piece of writing, comma splices and fused sentences make you look like an amateur!
To fix the problem above, you could put a period after shirt and begin all with a capital A.