No it is not normal to have all you are having. I suspect you have a thyroid disease brought on by pregnancy. Unfortunately it is more common than people realise. Go to the doctor and get full thyroid tests, these include TSH, Free T3, Free T4, and thyroid antibodies, known as Tg Ab, TPO, Ab and also a test called TSI. I suspect you have Hyperthyroidism.
Also
I have trouble staying asleep at night.
I am losing weight - but still have an appetite and eat well
I work out a I am not fatigued.
And I get heart palpataions sometimes