In this paper, we consider the problem of concurrent multipath routing and end-to-end entanglement distribution for online resource allocation in quantum networks. We propose a heuristic algorithm to solve this problem, considering quantum memory, decoherence time, entanglement distribution probability, and fidelity. A time-slotted quantum network operation model is considered based on the cut-off decoherence time of quantum memories. The proposed heuristic is designed for a quantum network with noisy intermediate scale quantum (NISQ) constraints, including fixed quantum memory decoherence time, and probabilistic entanglement generation and swapping. It considers integer linear programming (ILP)-based and heuristic approaches to select multiple paths and resource allocation in the network. Simulations are performed to evaluate the performance of ILP and heuristic based approaches in terms of requests using multipath approach, blocking ratio, and computation time in a small sized quantum network with few requests. Next, the performance of heuristic based approaches are evaluated for a large problem size. The obtained results ensure that performance of ILP and heuristic based approaches are comparable, and multipath routing outperforms single path routing in terms of blocking ratio.