I'm not sure who told you that you die to Christ when you receive Communion, but that's not really true. (That would be Baptism.)
When we receive the Eucharist, the saving power of Christ's death and Resurrection is applied to us and to our sins as we memorialize his death. St. John the Baptist called Jesus the Lamb of God.
Because in the Old Testament, the Jews were commanded to celebrate the Passover sacrifice, where a lamb was ritually slain and each family ate of it in the family seder and the blood of the lamb was placed on their doorposts. Those who did this were saved from the angel of death (Well, the firstborns were). Jesus is the Passover Lamb. 1 Corinthians 5:7-8 says,
7 Therefore purge out the old leaven, that you may be a new lump, since you truly are unleavened. For indeed Christ, our Passover, was sacrificed for us. 8 Therefore let us keep the Festival, not with the old bread leavened with malice and wickedness, but with the unleavened bread of sincerity and truth.
1 Corinthians 5:7-8
This is talking about the Eucharist. It was insufficient for the Jews to just sacrifice the lamb; they had to eat its flesh. Jesus was sacrificed on the Cross, but now we need to eat his flesh to apply that sacrifice to us; that's what the Eucharist is all about. This is why the Psalmist calls the Eucharist the cup of salvation (Psalm 116:13). So I think you are on track in what you believe.
The Eucharist is indeed a memorial but it's more than that; the term Jesus uses for memory is anamnesis, which has sacrificial overtones to it. It's a memorial sacrifice; a making present of the one sacrifice of Christ.
The Synod in Constantinople (January 1156 - May 1157) said,
"Today's sacrifice is like that offered once by the Once-begotten Incarnate Word; it is offered by Him (now as then), since it is one and the same sacrifice."
As for receiving the Body versus the Body and Blood, St. Paul tells us in 1 Corinthians 11:27,
27 So then, whoever eats the bread or drinks the cup of the Lord in an unworthy manner will be guilty of sinning against the body and blood of the Lord.
1 Corinthians 11:27
So if we eat the bread or drink the cup, in either case, we are sinning against the Body and the Blood of the Lord, so St. Paul was equating either form of Communion with receiving both the Body and the Blood. Therefore there is no obligation to receive both forms.
Receiving both forms is a fuller sign, but biblically it is not required. (As for Jesus, remember that the Apostles were bishops and priests, who always receive under both forms, then and now.)