In this study, the radiation characteristics of nonlinear Thomson scattering were investigated using the Lagrange-Gaussian model. Through analysis and experiments, we obtained the spatial motion trajectories of individual electrons and generated three-dimensional radiation data within the laser field. The results indicate that, under the conditions of a fixed operating wavelength, waist radius, and pulse width, electrons within a tightly focused linearly polarized laser field exhibit oscillatory motion in the x-z plane, forming a "zigzag" pattern, with the maximum displacement along the x-axis. Additionally, for the first time, we employed a time-resolved observation method to observe the three-dimensional radiation changes resulting from the interaction between the laser and electrons. We found that the normalized radiation energy exhibits different growth rates as the normalized time increases. Furthermore, within the laser field, the angles Φ and θ of the normalized peak energy are not fixed; only when the normalized peak energy tends towards its maximum value of 1.45 hundred million, the observation angles become fixed. These results are of significant importance for understanding nonlinear Thomson scattering and advancing research on X/γ-ray generation in optical laboratories.