Sensor-based local inference at IoT devices faces severe computational limitations, often requiring data transmission over noisy wireless channels for server-side processing. To address this, split-network Deep Neural Network (DNN) based Joint Source-Channel Coding (JSCC) schemes are used to extract and transmit relevant features instead of raw data. However, most existing methods rely on fixed network splits and static configurations, lacking adaptability to varying computational budgets and channel conditions. In this paper, we propose a novel SNR- and computation-adaptive distributed CNN framework for wireless image classification across IoT devices and edge servers. We introduce a learning-assisted intelligent Genetic Algorithm (LAIGA) that efficiently explores the CNN hyperparameter space to optimize network configuration under given FLOPs constraints and given SNR. LAIGA intelligently discards the infeasible network configurations that exceed computational budget at IoT device. It also benefits from the Random Forests based learning assistance to avoid a thorough exploration of hyperparameter space and to induce application specific bias in candidate optimal configurations. Experimental results demonstrate that the proposed framework outperforms fixed-split architectures and existing SNR-adaptive methods, especially under low SNR and limited computational resources. We achieve a 10\% increase in classification accuracy as compared to existing JSCC based SNR-adaptive multilayer framework at an SNR as low as -10dB across a range of available computational budget (1M to 70M FLOPs) at IoT device.