I have a Minimed CGM and it is very very very important to only calibrate when you have not eaten anything and not when you are experiencing a high or low blood sugar. It will cause the exact things you are mentioning. I calibrate 3 times a day. Two times isn't enough to calibrate because then you miss the whole middle of the day.
This is how I do it.
I wake up I check my blood then I calibrate...
Then at about 4pm I will calibrate again. It is enough time after eating lunch and before dinner to get the sensor really working well.
My next calibration isn't until right before I go to bed around 11pm. It is a good time to calibrate too because I eat dinner at around 6-7pm and the CGM won't wake you up at 3am to calibrate which is probably what is happening to you because you only calibrate 2 times a day. The way I do it overrides the automatic calibration in the pump.
It has only been a couple of days since you are wearing it you have to get yourself on a schedule with it and learn the alarms etc.. and work it out for your own body as well.
I have also had pain in certain areas of my body where it hurts more than others. I noticed the higher up in my abdomen the more it hurts and my CDE said sometimes the way you inject it in may not be at an actual 45 degree angle and that may cause the pinching feeling you get. Sometimes you hit capallaries too and the site will bleed. I have had all these kind of things happen.
As far as your lows there is a lag between the cgm and when you actually become low. For me it was a lot of trial and error but I finally have it down. I was writing down all of my lows and what the cgm said. I then noticed when I was at 90 on my pump, my finger stick was 70 so I put the low setting on the cgm to 100 this way it starts beeping before I am hitting the 70 and there is time to do something about it.
Now, If you have high readings during the night that are driving you crazy you can set your HIGH setting to 250 or above... this way you arent waking up a lot. It will only start alarming if you are low which is more important when you are sleeping. The beeping does drive me crazy as well but you can also put your setting to vibrate.
When you signed up to get the CGM you knew it wasn't going to be easy. It is still a piece of machinery that isn't perfect adjust it to your schedule and what your body tells you and you will see that the CGM will work to your benefit.
Hope this helps.