Just wanted to chime in that yes, stretching your calves can help your arch-heel-achilles-calf-hamstring system.

For a couple of months I was having heel pain, turned out my ankle/heel were taking turns fighting out of alignment and the chiro nudged them back in place. But, you know that's just a sign of bad muscles or will lead to bad muscle memory, so I was doing a lot of stretching. If they are sore/inflamed, use ice for about 15 minutes. I "cured" mine with stretching and trying not to strike on my heels - it didn't feel right anyway.

I do downward dog, then alternate heel presses, focusing on different parts of each leg - either lengthening all the way with your heel to the ground while your other knee is relaxed (toes to the ground), or lengthening the back of your ankle while your toes are to the ground applying pressure (other leg straight but relaxed). You'll feel the first stretch in the back of your calf, the second stretch closer to your ankle. You can also get that second one by doing a semi-lunge, with your front foot stretching the back of your ankle/calf rather than going all the way into a lunge and stretching your hips.

Hamstrings are good to lengthen, too, at this point it's just kind of general practice for me to go all the way ankles to hips as all those systems really overlap and benefit from each other. And, you might want to stretch your shins, too. Boy, the body is complicated. I find by taking 5 minutes to stretch all of the systems vs. just spot-targeting what irritates me, I care for the whole system and don't let a neglected part fail.

Welcome to running! Don't be afraid to walk and cover greater distance than you can running alone, don't be afraid to walk if you don't feel like you can run any farther, gradually increase your running distance, and remember to be patient and have fun. (That last one is the hardest sometimes)