This is similar to the question "Can a character shove an enemy who is already prone?". If your character is prone, can you grapple or shove an enemy in range? I haven't read anything that says you can't shove or grapple while prone, but I wanted to make sure.
You are able to shove or grapple while prone.
The Basic Rules outline the prone condition:
- A prone creature's only movement option is to crawl, unless it stands up and thereby ends the condition.
- The creature has disadvantage on attack rolls.
- An attack roll against the creature has advantage if the attacker is within 5 feet of the creature. Otherwise, the attack roll has disadvantage.
Nothing here says you can't grapple or shove while prone.
Note: while the rules for prone say "The creature has disadvantage on attack rolls", grapple and shove do not use attack rolls! Instead, each of these say that "instead of making an attack roll", you make a Strength (Athletics) check. So you don't even have disadvantage to grapple or shove while prone!