I'm not so sure, but I'd go with "naosu" instead of "iyasu" because to me it sounds more like healing our problems and traumas in general, not only our physical health.
Also, I don't really know if watashitachi is necessary there, most of the time they wouldn't use the pronoun. Here it sounds clear to me without it. It would be something like:
時間は 痛みを直すのではなく 、それとともに 生きることを教えるだけです。
Jikan ha itami wo naosu node ha naku, soreto tomoni ikiru koto wo oshieru dake desu.
But again I'm not so sure, and I'm a student myself. But hopefully this is helpful.