With the advent of JWST, we can probe the rest-frame optical emission of galaxies at $z>3$ with high sensitivity and spatial resolution, making it possible to accurately characterise red, optically-faint galaxies and thus move towards a more complete census of the galaxy population at high redshifts. To this end, we present a sample of 148 massive, dusty galaxies from the JWST/CEERS survey, colour-selected using solely JWST bands. With deep JWST/NIRCam data from 1.15$\mu$m to 4.44$\mu$m and ancillary HST/ACS and WFC3 data, we determine the physical properties of our sample using spectral energy distribution fitting with BAGPIPES. We demonstrate that our selection method efficiently identifies massive ($\mathrm{\langle \log M_\star/M_\odot \rangle \sim 10}$) and dusty ($\mathrm{\langle A_V\rangle \sim 2.7\ mag}$) sources, with a majority at $z>3$ and predominantly lying on the galaxy main-sequence. The main results of this work are the stellar mass functions (SMF) of red, optically-faint galaxies from redshifts between $3Comment: 19 pages, 10 figures, published in MNRAS; view published article at https://academic.oup.com/mnras/article/530/1/966/7630203