Hi, Leyanis
When I am told a dream which someone shares with us, I consider how it can have a general Gospel and spiritual meaning. I do not mean what I offer to be a personal prophetic interpretation; but someone else might be able to give you a prophetic meaning, which God has shown him or her, for you. Also, we have people who can understand a more psychological interpretation or give you how it could have some kind of counsel.
You say that two of the pieces have come out, but one more stayed. To me, the pieces can mean sin problems which you have had. And when you got saved, the two came out, meaning God corrected a lot, simply by bringing you to Jesus. But the remaining piece shows how any of us in Jesus still needs more correction > Hebrews 12:4-11.
And you say there was pain in the pieces coming out, but not a major amount of pain. Well, Hebrews 12:4-11 says there is pain in God's correction. One translation says His correction is "grievous" > He can grieve our selfish nature as His correction gets rid of anything which still is selfish in us!! So, this is good pain, to be sure, if it means God is getting rid of our selfish nature > our selfish nature has helped to keep us available to doing wrong things and to keep on deeply suffering in weakness of our selfish nature.
And I might consider how there were three pieces, perhaps not enough to make a whole container made of the glass. This could mean how in sin we shared with others, in our sinning, no one person having all the parts or pieces of sinning in Satan's kingdom; and though the parts perhaps fit with those of other people, those parts were dead . . . love dead!! Ephesians 2:1-7 < God has made us alive in Jesus. The encouragement is that we do well now to get rid of anything which is still love dead, and get more into loving with one another Jesus people, as family > Ephesians 4:31-32.
Now we share with one another in God's love, instead, as "members of one another" (Romans 12:5, Ephesians 4:25). And we help each other to become more and more corrected and mature in Jesus > James 5:16, Galatians 6:1, Ephesians 4:15-16.