HI,
That is indeed concerning to have a rapid and sustained low such as what you described. If you did indeed hit a vein during injection, there is not much you can do once the injection is in(besides eating to keep your sugars up for the time being). Be sure to take some mixed foods too to help sustain the glucose levels: glucose tabs are good for the short term but the effect will run out, so take something else(like half a sandwich) as well as the tabs.
Try a different site and pinch a decent roll of skin, pull it out from your body. This may help avoid any veins.
Take care.
Believe it or not, this happened to me yesterday. I take 85 units of Lantus in the am, and I think I hit a vein. As the injection went in, I didn't get the "burn", and I could taste it in my mouth. About a half hour later, I started to crash....450 grams of carbs later, I got my sugar up to about 200. It settled down a little later to about 140. As an RN, I should know better to pull back on the syringe to check for blood return before injecting. I was in a hurry...and won't forget to do that again!