Sickle cell anemia, which is also called sickle cell disease (SCD), is a hematological disorder that causes occlusion in blood vessels, leading to hurtful episodes and even death. The key function of red blood cells (erythrocytes) is to supply all the parts of the human body with oxygen. Red blood cells (RBCs) form a crescent or sickle shape when sickle cell anemia affects them. This abnormal shape makes it difficult for sickle cells to move through the bloodstream, hence decreasing the oxygen flow. The precise classification of RBCs is the first step toward accurate diagnosis, which aids in evaluating the danger level of sickle cell anemia. The manual classification methods of erythrocytes require immense time, and it is possible that errors may be made throughout the classification stage. Traditional computer-aided techniques, which have been employed for erythrocyte classification, are based on handcrafted features techniques, and their performance relies on the selected features. They also are very sensitive to different sizes, colors, and complex shapes. However, microscopy images of erythrocytes are very complex in shape with different sizes. To this end, this research proposes lightweight deep learning models that classify the erythrocytes into three classes: circular (normal), elongated (sickle cells), and other blood content. These models are different in the number of layers and learnable filters. The available datasets of red blood cells with sickle cell disease are very small for training deep learning models. Therefore, addressing the lack of training data is the main aim of this paper. To tackle this issue and optimize the performance, the transfer learning technique is utilized. Transfer learning does not significantly affect performance on medical image tasks when the source domain is completely different from the target domain. In some cases, it can degrade the performance. Hence, we have applied the same domain transfer learning, unlike other methods that used the ImageNet dataset for transfer learning. To minimize the overfitting effect, we have utilized several data augmentation techniques. Our model obtained state-of-the-art performance and outperformed the latest methods by achieving an accuracy of 99.54% with our model and 99.98% with our model plus a multiclass SVM classifier on the erythrocytesIDB dataset and 98.87% on the collected dataset.