ERJ 145 First Officer reported wind shear and severe turbulence on final approach due to a thunderstorm; resulting in uncontrolled airspeed and altitude. The flight performed a go around and diverted to an alternate airport.

Narrative

We were on final approach; cleared the ILS XXL; just initiated descent. The TS cell had been moving onto final and over the approach end of the runway. We had made the decision to go around. Immediately after we had a windshear warning and the autopilot kicked off. As pilot flying I was monitoring the flight path and doing my best to arrest descent. We encountered severe turbulence as we flew into the cell that had moved over the field at that point. Flap 22 limitations exceeded during the escape maneuver. Unable to maintain control over altitude and airspeed in the severe turbulence; climbed to and leveled at 4000 ft with 250 kts exceeded momentarily as well. There was Aircraft Y on frequency as well; I think some of the calls and read backs may have been confused back and forth with tower when getting missed instructions. Made the switch over to approach and put onto a downwind; autopilot reengaged. We came very close to and got a traffic alert to another aircraft. Autopilot was disconnected and I hand flew a sharp left turn to avoid. Further climb to 8000 was given when diversion to ZZZ1 started. CA took control as PF and I resumed as PM. Standard diversion and approach to ZZZ1 runway XY was made from there.