I have been diagnosed with Ulnar nerve entrapment. Is it possible to have carpal tunnel as well? It feels as if my whole hand is numb and tingling

CTS and Ulnar Nerve. entrapment can occur in the same limb. The ulnar nerve can be entrapped in more than one place as well (canal of Guyon in the base of the hand and cubital tunnel in the elbow. There are also other conditions to consider (Martin Gruber Anastomosis and "All median Hand Syndrome" ) A good quality EMG-NCS done by an experienced neurologist (or PMR MD) can sort this all out.
Certainly. An EMG study will conclusively document the presence of two nerve lesions, if indeed this is the case. Have your doctor order the testing.