Yes. The foreskin is attached to the penis "head" by a thin fold of skin named "frenulum" . During sex this gets torn and it especially happens in sex which is hurried, forceful and clumsy.
This heals well if given time. After healing you can attempt sex again and if needed use lubrication to have a smooth entry and thus overocme your fear.
Next Steps
As guys get used to vaginal sex, this frenulum gets flattened and it doesnot pose a problem later in life. So dont worry. Just go for sex with some ease.