[quote=@Norschtalen]
I'm not sure if I can make any attacks while grappled/restrained by the monster. 
[/quote]

[quote=PHB p.292]
[b]Restrained[/b]
[list][*] A restrained creature's speed becomes 0, and it can't benefit from any bonus to its speed.
[*] Attack rolls against the creature have advantage, and the creature's attack rolls have disadvantage.
[*] The creature has disadvantage on Dexterity saving throws.[/list][/quote]You are not forbidden from attacking. You just are worse at it.