We present an extensive analysis of the optical and ultraviolet (UV) properties of AT 2023clx, the closest optical/UV tidal disruption event (TDE) to date (z = 0.01107), which occurred in the nucleus of the interacting low-ionization nuclear emission-line region (LINER) galaxy, NGC 3799. After correcting for the host reddening (E(B-V)h = 0.179 mag), we find its peak absolute g-band magnitude to be -18.03 ± 0.07 mag, and its peak bolometric luminosity to be Lpk = (1.57 ± 0.19)× 1043 erg s-1. AT 2023clx displays several distinctive features: first, it rose to peak within 10.4 ± 2.5 days, making it the fastest rising TDE to date. Our SMBH mass estimate of M¯BH ≈ 106.0 M⊙ - estimated using several standard methods-rules out the possibility of an intermediate-mass BH as the reason for the fast rise. Dense spectral follow-up reveals a blue continuum that cools slowly and broad Balmer and He ¯II lines as well as weak He ¯Iλλ5876,6678 emission features that are typically seen in TDEs. The early, broad (width ∼15 000 km s-1) profile of Hα matches theoretical expectations from an optically thick outflow. A flat Balmer decrement (LHα/LHβ ∼ 1.58) suggests that the lines are collisionally excited rather than being produced via photoionisation, in contrast to typical active galactic nuclei. A second distinctive feature, seen for the first time in TDE spectra, is a sharp, narrow emission peak at a rest wavelength of ∼6353 Å This feature is clearly visible up to 10 d post-peak; we attribute it to clumpy material preceding the bulk outflow, which manifests as a high-velocity component of Hα (-9584 km s-1). Its third distinctive feature is the rapid cooling during the first ∼20 days after peak, reflected as a break in the temperature evolution. Combining these findings, we propose a scenario for AT 2023clx involving the disruption of a very low-mass star (≲0.1 M⊙) with an outflow launched in our line of sight and with disruption properties that led to efficient circularisation and prompt accretion disc formation, observed through a low-density photosphere.