Hello,
All of your tapping phrases seem to be appropriate. It seems to me that his fear of abandonment might very well stem from the amount of time that he was left in the care of strangers for his medical issues. Even though, I am sure you were with him as much as was possible, the treatments were nontheless traumatic for him.
Consider that you may have some guilt issues about his medical issues and treatment. So tap for that. Also consider that he may be picking up on your anxious energy. Tap for that as well.
Additionally, tap for "you are safe", "you are loved", etc. It may sound the same as what you have been doing, however, sometimes tweaking things a bit can make a big difference. Developmentally, this is not an unusual reaction for a child his age. He may just be more sensitive than the average 3 year old and may need a little more hand holding.
Perhaps when you drop him off, you can wait outside until he settles or give him a picture of you to take with him. Hope this helps. Don't worry, he'll get the hang of it.