What kind of insulin is Oliver getting? Is he having these symptoms constantly or intermittently?
Is he on the same diet, eating the same amount of the same food as he was before he started insulin or was his diet changed?
Your story sounds like a cautionary tale for why cats need to be home tested. Three units of any insulin is a very high dose, and it is huge if you switched from a dry diet to low carb canned when he was diagnosed. Three units twice a day seems like the default starting dose for vets who do not advocate hometesting though, so I am not surprised. It's still too high for a starting dose, regardless.
I agree that it sounds a lot like Oliver is hypoglycemic, and at this point, long term hypoglycemic, several days. We think of hypoglycemia as what happens to people when they get shaky because they haven't eaten, but it is way more than that and is a serious condition in a diabetic cat, it can kill and it can permanently damage.
It sounds like he needs his glucose tested before he gets another drop of insulin. For home testing, you just need the least expensive glucose meter you can buy, and a small packet of strips; the meters usually come with a few lancets (or mine did). You can get the Relion meter at WalMart for $9 and the smaller package of strips for $12; lancets, if you have to buy them are about $4.00/100. There are a lot of basic instructions on how and where to "poke" on this site- on the ear, between the vein that runs along the edge of the ear and the edge of the ear, trying not to hit the vein. When I was testing Charlie, who was a big bad Siamese, I sat at the kitchen table with him on my lap, back towards me, front paws on the table. I had everything ready and gave him a freeze dried treat each test, the treat became more important to him than the poke and we got the time down to about a minute. "Wedging" him between the table and me, on my lap like a baby, eliminated the necessity to wrap him like a burrito or do anything else resulting in further trauma. I just did the poke from the back with a folded Kleenex in front of the ear, put the strip in the meter following instructions, held the spot where I'd poked with the folded Kleenex for a few seconds, then let him down. The calmer you are, the easier it will go and the quicker it will become routine.
Your other alternatives at this point are another trip to the vet for a glucose test or, even less optimal, stopping the insulin, watching to see if he acts better, then restarting the insulin at a MUCH lower dose (I'd start with 0.5u), keeping it there for 5-7 days, then trying a small bump up to maybe 1u, watching Oliver's behavior. This is what you'd do with the dose if you home tested and his first reading was low also, but you'd know what you were treating.
It's really nice to have a vet along with you for home testing, I was lucky enough to have one, but many people do not.
