Yes very possible indeed. In fact I feel the difference in about an hour or so since I have issues breathing with not enough thyroid hormone in the blood. I have gone from very hyper to very hypo in about a day or so but admittedly I have weird issues with my cells. :)
Shame on me - I forgot to mention that a lot of symptoms overlay/can apply to either hypo/hyper, so don't assume that because you have heart palps you're hyper - I had those when I was really hypo... I've also had low energy and been tired from B-12 or iron deficiency... have you had those checked? If B-12 isn't at the top of the range, you can feel like death warmed over. Iron needs to be relatively high as well.
These are all things to look at ... 12 mcg T4 thyroid hormone increase is quite small, so shouldn't cause a drastic reaction within 2 days... look at some other things and if you can rule them all out, then you may be reacting to a filler/binder in the thyroid med, which does happen, but is relatively rare.
You also have to look at supplements you might be taking that could be causing you to feel wired at night, such as B-12, D, DHEA, as well as some herbs - it all works in together, so you have to look at everything you're putting into your body, including your food. Are you drinking coffee or hot chocolate in the late afternoon or at night?
It depends on what med you're taking. If you're taking a T4 med, it takes 4-6 weeks for the dosage change to take full effect, though you might feel slight changes in symptoms within a couple days; going from full blown hyper to hypo and back within a couple days is pretty much not going to happen, though it's VERY common for symptoms to worsen or for new ones to appear when changing doses... you just have to stay the course for a few weeks and let the med do its thing.
A reaction within 2 days of a T4 med change is most likely either from anxiety (yes, we have it, even if we don't specifically "feel" it, because we tend to attribute it to other things) or from the fillers/binders in the med.