Thanks for using the forum. I am happy to address your questions, and my answer will be based on the information you provided here. Please make sure you recognize that this forum is for educational purposes only, and it does not substitute for a formal office visit with a doctor.
Without the ability to examine and obtain a history, I can not tell you what the exact cause of the symptoms is. However I will try to provide you with some useful information.
The median nerve runs near the area of where blood draws occur. It may be injured with blood draws for example. The symptoms may be pain/sensory changes in the thumb and first couple of fingers. When the area is stretched, as you mentioned, the symptoms worsen. Typically, the symptoms improve with time.
Thank you for this opportunity to answer your questions, I hope you find the information I have provided useful, good luck.