Merging gmail accounts

When my website was hosted with Wix.com I purchased Google services that included my company email account - kathy@brs - and allowed me to use Gmail to access my emails. After I closed my Wix website, I set up the same email address - kathy@brs - on BlueHost and I am getting emails there. I could see them in the BlueHost email system. But, I couldn't figure out how to set up this company email account to login via Gmail (even though BlueHost provides instructions to do so) because Google thinks I am still connected to Wix and will not allow me to change the source of my emails. So I had to create a new gmail account - kathybrs@gmail - and set up forwarding from my BlueHost email system. However, now I have emails in two systems and it makes it difficult to send calendar invites and use Google drive because clients will see the Gmail address v. my company address. I need someone to download all my emails off these two accounts, disconnect me from the Google/Wix service, and set up my primary email so I can login directly from Gmail. Thanks.