Extreme Calf Tightness After Running (it winds up like a clock spring, within minutes)

[finchr]

As you mentioned several times, the pain with running always came after lifting. Rather than try to continue strengthening through the pain, which sounds like it isn't working for you, try relieving the stress on the left achilles/calf by inserting a heel lift in your running shoe s. See if it doesn't relieve some of your discomfort.
It sounds like you are overstressing your calf muscles with the weights and since running is more on the balls of you r feet, it aggravates it further