At 2.5 months in I was still a nutjob having massive mood-swings, meltdowns, depression, and even some raging tantrums. I was lifting weights and running too!
The good news is all that leveled out eventually, somewhere between six months to one year. I did use exercise to tire myself out and that was really the best effect I reaped from it all -- slightly reduced anxiety levels, good sleep, and a sense of accomplishment. All of it contributed to raising my self-esteem back then. I did kind of push myself too hard at one point by running a race I wasn't entirely conditioned for, and by burning out on the running and lifting along the way.
These days, I'm content to run 3-5 times per week, around three miles or so and I'm done for the day. It's mostly become a meditative exercise for me. I am 32 months sober.