When You Think He Just Wants To Sleep With You

I met a new guy online. We FaceTimed on a Thursday, had first date Saturday, second Sunday and third Tuesday with another scheduled for Saturday. Every time I see him he asks when he can see me again. There has been great chemistry but I’m feeling overwhelmed. He asked what I was looking for, I said a relationship, he agreed but I’m feeling pressure from him to sleep with him even after I’ve told him he’s moving too fast for me. Am I right to feel overwhelmed? Am I being lovebombed? I am not sure what to do here as I like dating him but have the feeling he may only want to sleep with me.