If it's going to be constant rain, you should check out the outdoor section in Dick's for goretex gear. Some rain jacket form North Face or Columbia should work. Running jackets are not normally waterproof.

i might even consider a poncho from the camping section. Lots of ventilation and completely waterproof.

Have had success with finding items in those stores. Lived in UK for a few years so ran in a lot of rain. Jackets that worked for me were not necessarily water proof, though those are best if going to be soaked. Those are the gore tex ones or similar and will probably be on the more expensive side but check sale racks. Look for lots of vents (under arms, covered by flaps in the back, even zippers for heat release). Have had jackets not designed for exercise that don't breath and you get wet from the inside due to sweat! These tend to be a little heavier.

For running specific, like mentioned, they tend to be resistant versus water proof. This is OK for me as unless bitter cold rain, know I won't be totally dry so just looking for the barrier to prevent the cold drops from hitting me directly.

Also, as an added suggestion look for a jacket that converts to a vest. In the temps you describe, I would probably choose a vest just as a way to keep the shoulders, back, and chest covered from the rain and a little warmer but the body breathing a little better. May start with the full jacket then rip the arms off (usually zipper or magnetic).

You should be able to find something. Good luck.

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