Flying out of YVR to PUD to SGN on China Eastern

You need to take the doctors' note to prove that the insulin is really necessary. Then, take self-use amount of them with you. But I heard some airlines don't allow passengers taking this kind of medication themselves. You may contact your airline to find out whether you can do it or not.
As for contact solution, you should be allowed to take less than 100ml to the plane. Or, you may need to check it.