In the panorama of Bone and Muscle Conditioning (BMC), Forearm Conditioning ranks straight after Knuckle conditioning in order of importance. The ability of not just blocking, but even using your forearms as a weapon, is something that a Martial Artist shouldn’t underestimate.

If you consider blending Forearm Conditioning with proper Muscle Exercises, the sum of an extremely low pain threshold with muscle mass will noticeably increase your confidence in Sparring.
This is a common case when you start training Forearm conditioning for the first time. First of all: don’t worry: it’s your Ulnar nerve that has been targeted, that’s why you feel local numbness and tingles, although it may seem it’s your vein. The Ulnar nerve is the largest non-protected nerve in the human body (unprotected as not covered by muscle or bone), so it’s very common to injure it if you don’t proceed gradually. Second: interrupt your training immediately and read through this carefully: when you begin with your training session, you should take into account of three important factors: Intensity, Evenness and Angle of impact.
Are you a beginner? Are you starting your workout with power-hits instead of gradual hitting? Are you properly training your forearm muscles as well as conditioning them?
Are you focusing always on the same spot? Keep in mind that hitting is meant to be along the bone, not on the same spot all session long.
With regard to this specific section of BMC (Forearm conditioning) - yes - it’s true that you can decide to hit only your bones, or hitting just your forearm muscles by changing the angle of impact, but sometimes “the half way method” might cause a particular spot of your forearm to be more exposed to impact (the ulnar nerve in your case). So, in summary, keeping in mind that each of us has a different bone structure, the golden combination is always: train gradually + local massage.