Hi Emma
I'm very sensitive to insulin, I react very quickly to it and so I can only take very small doses. The maximum mealtime dose is 3 units which for me is 60g of carb or 75g in the evening, but I have to be feeling pretty brave to go higher than 2 units in the evening because I'm very prone to nighttime hypos. The basal testing might be a very good next step for you if only to rule out the possibility that you either don't need basal at all, or you need more. Once you know the baseline is correct it's easier to come up with strategies. I started out last year on a ridiculous amount of basal (30 units) and was hypo and then hyper constantly. I take 6-7 units of basal now. It was very hard work getting to the root of the problem though because i was rebounding a lot. I'm lucky my liver is quite keen and shoves out glucose to rectify the lows but it did obscure the problem quite a lot.
Incidentally I frequently inject mid meal which you may find helps as a short term solution it gives the food time to get going before the insulin hits. Longer term I did the following to find the actual problem. Fixed carb meals for a while, preferably if funds allow something carb counted independently (I used the M&S balanced meals because they're easy, and resemble actual food). If funds or family circumstances don't allow that then weigh everything and use the packets or carbs and cals to make sure you've got the exact amount of carb. That rules out one factor, namely that you're not estimating carbs correctly. I went for food that was mid level on fat, so there wasn't the high fat complication in the mix. Go for around 40-50g of carb, on the basis that the amount of insulin for that amount should be conservative enough to prevent a hypo. Pull your ratios right back, I went to 1:30 to start with but you might want to do 1:20 say and then test every 30 minutes (to see how you respond to food and insulin which helps to work out if it's just a timing issue rather than a dose issue). This most likely won't be enough insulin but even the high reading later will tell you something. If you're like me then the reading you get after the meal will be lower than you're used to which shows you that you were rebounding before. I was actually rebounding most of the time, then I'd having major hypo clusters, which I now realise was when my body was depleted of glucose stores. Its counterintuitive to take less insulin when running higher blood sugars but I was going utterly insane with it all, and like you feared injecting rapid because it was it was like trying to control a tsunami (that might be exaggerated to some reading this but I was at breaking point by this stage). I wish I could say my medical team provided lots of help and advice but they didn't, they were pretty useless because honestly I don't think they had any idea about insulin sensitivity. The exercise above helped me identify the issue and once I'd got my ratios sorted (not the 1:10 the DSN and consultant insisted was perfect) it helped me prove to them that I knew how to count a carb, that the maths wasn't beyond me, and I wasn't hysterical. Which was actually the starting point for useful help from them. It's also how I worked out where my ceiling is for insulin amounts. I did so basal testing first though and reduced the basal quite a bit before that point.
Anyway not sure if any of that is helpful, but I wanted to write it because I empathise with how you're feeling right now and wished someone had told me that we don't all conform to the same model when I was at the end of my rope 🙂