I totally back up Nigel that it's a good idea to raise this with your diabetes team, but I also wanted to say that hypo symptoms are very very individual and very very varied. I usually don't get symptoms from the list you gave, but I do get good hypo awareness; my symptoms are just different from textbook lists, and often it's just a question of a sort of sixth sense that I'm hypo. I couldn't even put it into words.
So, I wouldn't be ruled by a list of only a few symptoms - if you know you are hypo because of a 'symptom' that isn't on the list, you still have hypo awareness.
HOWEVER I think if you are dropping to 2 and only picking it up by chance or by regular testing, eg you are surprised at the reading because you didn't know you were dropping low, then you have lost awareness and it's worth finding someone who can help you.
The good news is that most people manage to get some symptoms back by avoiding hypos very carefully for a few months (you may need to run a bit higher than normal for a while). Others on here have also talked about going onto animal insulins - search for 'porcine insulin' - I personally don't have experience of that so I can't comment.