You can absolutely use both Photoshop and illustrator and in fact, if you are working in industry in a full-time job, most companies will require that you know how to use both of the programs. And the thing is, each of the programs is better for different things.
Illustrator and Photoshop are both part of Adobe Creative Cloud and are designed to work together. Photoshop files can incorporate assets made in Illustrator, integrating an image created as a vector file into a raster file.