Hi salsa,
Two distal areas where entrapment of the ular nerve can happen are the medial elbow where the nerve wraps underneath the medial epicondyle or through the ulnar aspect of the wrist where the Ulnar nerve goes through Guyons canal.
Prolonged time with the elbow bent, sleeping on it or leaning on the point of the elbow (on the phone) can compress the nerve and cause irritation. Increased sensitivity can arise from hitting this area (off the edge of a table) etc causing inflamation and subsequent irritation. tapping over this site may increase tingling down the arm.
Entrapment through Guyon;'s canal can be similar to carpal tunnel, resulting from repetitive stress/compression of that side of the hand or trauma.

Both would probably require a consistent amount of pressure directly on the nerve, repetitive trauma or possibly some bony deformity to give symptoms to this area. If this sounds like something that may be happening to you working/sleeping then changing technique/using appropriate padding over the area should help decrease the pain and your physio should be able to show you some gentle ulnar nerve mobilisations to help the nerve heal.

However, i think you may need to get your physio to look higher up (if not done so already) in the cervical spine on that side. This may be more likely a cause of your pain in the hand than triggerpoints in the shoulder/forearm, as referral into these 2 fingers is fairly specific and if you spend a lot of time at a computer there's a good chance you've got poor posture, rounded shoulders and are at an increased chance of compressing the joints in your neck. Also generally in referred pain from muscles resistance exercises are more likely to make the pain worse rather than better.

Really you and your physio need to identify where along the course of the nerve is the greatest irritation, what exactly brings on the pain and work on improving mobility/relieving stress. Your physio can monitor your mobility using the Upper Limb Tension Tests and invent some gentle "slider" techniques to help and also mobilise any restricted joints alond the way.

I would continue the same gym work (no harder yet), as long as it's not irritating you and work on your scapular position and posture. Once the problem is identified, progress can be slow and steady over a few weeks. If no progress is made at this stage or if you experience any muscle wasting or loss of sensation/weakness i would go see a specialist.
Good luck with this, let us know how your progressing.