Hi Cris, welcome to the forum 🙂 It's often the case that people feel perfectly well with higher than desirable blood sugar levels, and this is one of the reasons that many people with Type 2 don't get diagnosed for a long time. However, the higher levels will possibly be causing longer term damage, so it's best to try and get them down. From what you say, it sounds like you've pretty much succeeded! Your waking levels are ideal in the mid-5s and your post-meal levels are pretty good too, so I don't really understand why your nurse wants you to get them lower.
The reason you feel bad at these kinds of levels is that your body has got used to the higher levels over a long period of time and now your brain thinks that you don't have enough glucose in your blood so is sending out 'warnings' that have the effect of making you feel weak, dizzy and shaking. These symptoms should disappear after a while, as your body adapts and your brain stops 'panicking' so don't imagine that you will always feel like this! Eventually, you will feel just as well as your did at the higher levels, but without risking possible diabetic complications. 🙂
If you have any questions, please don't be afraid to ask - nothing is considered 'silly', and there is usually someone around who can help!