Estimating a soft robot's pose and applied forces, also called proprioception, is crucial for safe interaction of the robot with its environment. However, most solutions for soft robot proprioception use dedicated sensors, particularly for external forces, which introduce design trade-offs, rigidity, and risk of failure. This work presents an approach for pose estimation and contact detection for soft robots actuated by shape memory alloy (SMA) artificial muscles, using no dedicated force sensors. Our framework uses the unique material properties of SMAs to self-sense their internal stress, via offboard measurements of their electrical resistance and in-situ temperature readings, in an existing fully-soft limb design. We demonstrate that a simple polynomial regression model on these measurements is sufficient to predict the robot's pose, under no-contact conditions. Then, we show that if an additional measurement of the true pose is available (e.g. from an already-in-place bending sensor), it is possible to predict a binary contact/no-contact using multiple combinations of self-sensing signals. Our hardware tests verify our hypothesis via a contact detection test with a human operator. This proof-of-concept validates that self-sensing signals in soft SMA-actuated soft robots can be used for proprioception and contact detection, and suggests a direction for integrating proprioception into soft robots without design compromises. Future work could employ machine learning for enhanced accuracy.