Yes, you are worrying for no reason. The only person who must consume both the Body and the Blood of Christ is the priest.
When we receive under one species only we receive both the Body and the Blood. The elements (bread and wine) are consecrated seperately. This shows the seperation of body and blood.
For hundreds of years, the laity never received the Blood of Christ - there is much more likelihood of accidents while receiving from the Chalice. Besides, it is necessary to be very careful with the quantity of wine that is to be consecrated, since the Blood cannot be placed in the Tabernacle, as can extra Hosts.
It is only in the years since Vatican II that the laity have been allowed to receive from the Chalice, and, even then, not always. More recently, it is permitted to do this more frequently, but still not when the size of the congregation would make it difficult to determine the correct volume to consecrate, and also, when the number of people to receive would make it difficult to manage appropriately.
Fear not - you receive the whole of Jesus when you receive only the Host.