Upgrading from a Nikon D3200 to a full frame?

I've been shooting with a D3200 for 2-3 years now and it's worked well for me so far. However, I plan on pursuing photography professionally (that's my major) and I believe I'm due for an upgrade. I mainly shoot portrait, in-studio and fashion, and some landscape (also my dog and other animals, but that probably doesn't matter). I want to purchase a full-frame, but I don't want to sell my soul in order to afford it. Is it worth upgrading to a full frame? I was thinking D600/700. The lenses I use the most are 35mm and 85mm.

It may be, but first I'd suggest, given your preferred genres, that you upgrade your glass AND invest in some off camera lighting and modifiers - you'll get far more bang for your buck than upgrading the body.

And as a portrait/fashion photographer you need to have (and learn to use) off camera lighting.

Deep blue2 is correct.

I shoot a whole lot of fashion and the two most important tools needed to do that are knowing how to light the models and how to direct them.

For many years I used a Nikon D300 to shoot fashion and that APS-C sensor was NOT a hindrance, since almost all of the shots were to be used on websites

The D700 is still a viable camera (I have one I use when I'm shooting in hostile environments), but wait until you have all your lighting gear before you spend any money on a full frame camera. If you can save your pennies so you can budget for a gently used D800e, you will be able to increase the resolution of your fashion photos.

If you have to sell your soul to afford an FF camera then you're not ready for it yet. Use your existing camera to earn money for your dream camera. Shoot professionally with that entry-level. There's no shame in that!