As you know, it is a natural thing to happen, therefore, with my own cats, I haven't paid much attention to it, just let the cat get over it. I don't know if there is any pain involved in it, but to my understanding the meowing is more a call for any toms in the neighborhood. If pain was part of the matter I would still not medicate the cat in any way, since it is natural, and medicating the cat would be more for my own peace of mind than for the cat's ease.
Beware of possible escape attempts, especially if there is a tomcat nearby answering to your cat's calls. A female cat in heat, hearing a tomcat answering to her, may summon tremendous strength and agility to conquer any obstacles in her way outdoors to mate. The first heat of a young cat is yet weak, but in later heats the cat may become hard to handle.
Spaying the cat would be a good, and permanent, solution to her anxiety, but is it quite answering your question "...through the estrus cycle?" because spaying effectively removes most of the cycle. However, that is what I've done to my cats after one or at max three heats. Much easier for everyone and actually it is good for the health of the cat.
Indoor cats who don't get to mate while in heat have a chance to go into heat again quite soon, possibly as soon as two weeks after the previous heat period ended. There is a variety of risks to the cat's health involved with each heat cycle, for example an infection in uterus and breast cancer, so eventually spaying your cat would benefit both her and you, and even your neighbors with the reduced number of loose tomcats circling and spraying your house and the houses of your neighbors.