People tend to train in Martial Arts for many different reasons, though none of which are to damage themselves. Therfore you need to train with that in mind, you cannot defend yourself well if you are injured with an unsafe practice or training method.
With the variety of Martial Arts styles that exist, it is hard to cover the different types of injuries you may encounter. Impact sports will suffer bruising for example, and grappling styles will probably result in the same, however quite often people will experience overstrains. Anything with a 30%+ Methyl salicylate concentrate in such as Tiger Balm will help to ease muscle strain, and of course make sure you rest, ice, compress and elevate. If these basic first aid principles do not suffice then please ring up to book an appointment.