Can you have carpal tunnel syndrome even if your emg test was normal as well as your blood test ?

Carpal tunnel: Unlikely. The EMG is sensitive to any type of nerve injury or damage (which is what CTS is - the median nerve is pinched at the wrist). So it is unlikely since it is such a sensitive test. Assuming the test was done correctly - I would be looking at other causes for your symptoms - maybe in the neck??

Possible: Early on, the symptoms could be present but not enough damage yet to result in EMG changes. An ultrasound study might be a better demonstration of narrowing at the transverse carpal ligament.