Has the Church formally declared that Jesus is fully present under the appearances of both bread and wine?
This instructor needs to take some basic instruction in the Catholic faith before she tries to teach others. She’s wrong on both counts. First, the Church has formally defined the doctrine that Jesus is completely present, body and blood, soul and divinity, under the appearance of the consecrated bread or the wine. This doctrine was officially taught by Pope Martin V in 1418 in his bull Inter Cunctas and formally defined as dogma at the councils of Constance (1415), Florence (1439), and Trent (1551), and it was reiterated at Vatican II (Instruction on the Worship of the Eucharistic Mystery, 32).
For the clearest biblical evidence, look at 1 Corinthians 11:27: “Therefore, whoever eats the bread or [not “and”!] drinks the cup of the Lord unworthily will have to answer for the body and the blood of the Lord.” This means that reception of either the host or the wine carries the same reality of Jesus’ body and blood.