Parent visa application UK - Overstayer

[Ukukuk1718]

Hi everyone,
I came to the UK on a visitor visa is 2012 (I overstayed my visa) , I had a baby with a british women in October 2017, therefore my child has British citizenship. I sent off my application with all the info in March 2018. I recieved a letter that the home office received my application and I did the biometric finger prints etc. Does anyone know how long I can expect to wait for approval? I need to be able to provide for my daughter and partner! Would it be worth contacting my MP in a few months?
Thanks, hopefully you can all advise me!

[Ukukuk1718]

Also I do not live with my partner.

[CR001]

Are you still in a relationship with your partner even though you do not live together??

[Ukukuk1718]

Yes, we are in a relationship, but only boyfriend/girlfriend not wife/fiancée etc. And she is going to uni in September.

[Ukukuk1718]

Are you still in a relationship with your partner even though you do not live together??

Yes but we have been together less than 2 years.