When an agent or editor asks to look at a full manuscript, give them three weeks to look it over before calling or emailing. Three weeks may be a lifetime to you when you're waiting for a response, but in publishing it goes by in a flash.
When that agent or publisher receives your manuscript, they likely have a few other manuscripts in queue. Be patient. And if they say to not expect a response for a certain amount of time, then wait that time.
Being pushy and a nuisance only gives the agent or editor a good indication as to how it might be to work with you, and no one wants to work with someone who can be annoying and doesn't respect timelines. Be cool, calm. Write some more. Just wait. It will only work in your favour.
And don't think you're being cute or friendly by sending a quick email asking how things are going. It's not cute or friendly. It's passive aggressive behaviour that is not welcome!