So in RAW, having a creature between the attacker and a target grants the target half cover, but I'm a grappler that likes to shove down my victims while grappling. Do I still get the cover bonus for having a creature between us if he's prone in RAW? I'm worried that my DM will overrule because it doesn't make physical sense if he's prone to also provide cover.
A creature might provide cover. A prone creature probably won't.
Here are the rules for half cover:
A target with half cover has a +2 bonus to AC and Dexterity saving throws. A target has half cover if an obstacle blocks at least half of its body. The obstacle might be a low wall, a large piece of furniture, a narrow tree trunk, or a creature, whether that creature is an enemy or a friend.
(Emphasis mine, PHB, p. 196).
So the rules as written aren't that a creature between the attacker and target always grants half cover; it's that such a creature can grant half cover.
A prone creature probably doesn't block at least half of a standing character's body, and so it wouldn't provide half cover. Similarly, a standing halfling doesn't provide cover for a half-orc standing behind it.