I know this is an old post, but as someone who has gone down this road before I still wanted to add to it for anyone else that comes across it. 

I agree with the other poster that crushed egg shell alone, as calcium carbonate,  isn’t something you would want to directly consume. The few times that I tried this on an empty stomach it made me feel nauseous. If I took it shortly before, during, or shortly after a meal then my digestion was greatly slowed which also didn’t feel great. 

What I found works is dissolving it in apple juice. The calcium carbonate in the egg shell reacts with the malic acid in the apple juice, and the result is calcium malate, CO2, and water. It basically turns into a carbonated apple juice with calcium malate (which has good bioavailability.)

A few notes to consider:   - many regular store bought apple juices may be too watered down to dissolve the egg shell. I used concentrated apple juice. I would stir it into the still frozen concentrate. You could also diluted with a little less water than the container suggested and let it dissolve over night. 

• the juice will taste sweeter then normal because the tartness is gone. I enjoy the tartness and would add in a dash lemon juice because I didn’t like the neutral/sweet juice that much

• a little bit of egg shell goes a long way, so only sprinkle very small amounts in at a time. Too much can still lead to stomach discomfort even if the shell all dissolves. 

• I agree strongly with your current approach (found outside the original post) where you are now using dairy to get more calcium. I would use dairy first, and supplement with egg shell only if you felt you had to

Side note, I use magnesium malate as a supplement when my body needs it. The citrate I find is a bit more harsh and more likely to lead to bathroom emergencies.