Recommendations to upgrade from my Nikon D3200?

Hello, I’m an amateur photographer currently working with a Nikon D3200 but am wanting an upgrade! A lot of my pictures are coming out grainy no matter the iso, aperture etc and so to go more professional I know I need a better camera or lens.

I currently do travel and portrait photography, and have done one wedding! I mainly do children and pets for my portrait photography so need fast shutter speed!

I have tried a Fuji X-T2 and didn’t like it, I prefer a point and shoot as compared to fiddling with manual settings every time! And I do just like Nikons, but wouldn’t rule out other brands.

I would like a touch screen I think this time if possible.

My budget would be around £500-£750. Thanks in advance!