No, higher pressure does not push you upwards. That's all about buoyancy and a liter of water weighs just as much at the bottom of the ocean as it does at the surface. That higher pressure works on all sides of your body which means it cancels out.
Edit: Found a direct quote on wikipedia https://en.wikipedia.org/wiki/Properties_of_water#Compressib...: >The low compressibility of water means that even in the deep oceans at 4 km depth, where pressures are 40 MPa, there is only a 1.8% decrease in volume.[40]
Thank you for correcting this.
Near the surface it’s almost never an issue, but for ultra deep dives it’s important.