The chance of you hitting a vein or other blood vessels would be very low, but it is always a good idea to insert the needle and pull back on the plunger to make sure no blood goes into the syringe. Injection into the blood vessel could cause more of an allergic reaction or anaphylactic shock. This would be very unlikely though. Don't "dart" the needle in. Just inject it into the skin, gently. Put the needle into the skin in one motion. With an insulin syringe, you probably won't have to worry much about it. The needles are usually small. Just push the plunger in steady, as quick as the fluid goes. That is all you need to do.
If you see blood come into the syringe, just redirect the needle to a different spot (without removing the needle from the skin) and inject. If there is some air at the end of the syringe nearest the needle, just lightly flick it with your finger to make all the air go near the needle, then lightly push in the syringe plunger until the air is out, then inject the needle into your kitty