Going to the gym should be an important feature of your training week. Gym training will help build muscle strength and stamina which can help prevent injury. However, simply pushing weights and building up your muscles isn’t necessarily the right approach as bigger muscles mean more weight to carry around while running. Also working by yourself in the gym often leads to you underworking and then rewarding yourself for the effort later (mmm, cake!). So a better approach may be to take part in a circuit training class such as Body Pump.
These tend to use low weights but high repetitions so your muscle mass doesn’t build hugely. These also have exercises that develop-p your core muscles (i.e your stomach). Not only will this help you look better but it will improve your running efficiency as your body will hold its form better when running and you won’t slouch as much towards the end of a run. Slouching effects your breathing (ask any singing coach!)