Strange and sudden hypo caused by basal insulin?

That doesn't sound good.
A few things to think about
When was your last meal; rapid insulin can still have an effect some hours later?
Alcohol?
When was your last exercise? when this happens to me it is usually because I had some late afternoon/early evening exercise and didn't take this into account sufficiently with my insulin at dinner
Lastly and this is a bit nebulous, sometimes in the early days the pancreas still has some function and can be a bit sporadic about when it decides to 'help' you out with a bit of insulin.
I don't think that I have ever thought that I might have done an intramuscular rather than subcutaneous injection but if you are very thin this could be a possibility. (think a vein is unlikely with a tiny pen needle)
The high may be just from over correcting (it's hard to take the dextrose and wait after treating when you feel like that) but your liver may also have thrown in some glucose as well.
I wouldn't start injecting extra basal insulin, and even using some more bolus may not be a good idea. Too much and you will end up bouncing from high to low.
(besides when and how much is very individual , you really need your doc/nurses advice here and indeed you really ought to contact them for advice)

I've had a couple of hypo's as you've described and I've put them down to two possible factors:-

Not shaking the pen before injecting.
Injecting into a muscle by accident.

There are still some fine veins around the subcutaneous injection sites (as you'll possibly know from catching one and bleeding / bruising now and again). If you got really unlucky and caught one and injected straight into the vein, the insulin would kick in very quickly. It'd be spectacularly unlucky but might just be possible

Yes, this has happened to me too. i inject my basal insulin in the morning and a few months ago after having my basal injection i was just about to have my breakfast (I always inject bolus post meals) when I felt slightly light-headed so I tested my blood and I was 2.7! Bearing in mind one hour before I was 8.8. I had a drink of Lucozade and then ate breakfast and my BG gradually came back up.

The only thing I had done differently that morning was inject the basal insulin into my thigh. I always injected into my stomach previously but the day before I had seen my DSN and she said start injecting into your thighs as well. I think this was the reason, I must have gone into the muscle. I haven't injected into my thighs since. Hope you are ok now, its a bit scary isn't it?

Regards
Annie.

Any chance you took your bolus instead of your basal insulin. I've done it twice!

It's unlikely to be caused by basal. Basal insulin has been designed to crystallise once injected. It then slowly disolves throughout the day. It certainly won't cause a hypo 10 mins after injecting, even fast acting insulin isn't that fast acting.

Agree ... Very, very unlikely to be your basal..
Basal is designed to work on a slower release system in our bodies. I expect its coincidence it happens around times of basal injections..

These lows will normally be due to too much short acting insulin, and possibly another factor such as not enough carb, exercise during previous 12 hour, etc.

I suspect that everybody mentioning these hypo's coming on rapidly will have had a food bolus within 3 hours prior to the hypo...