ERJ 170 Captain reported a wind-shear encounter which led to an altitude deviation on the missed approach. Captain reported that the First Officer was flustered and unable to select appropriate modes of automation; flap configurations or respond to radio calls for the remainder of the flight.

Narrative

Upon landing in ZZZ on ILS XX Right; we faced wind conditions of 190 degrees at 20 knots; gusting to 33 knots; with a wind shear advisory in effect. As we descended through 20 to 10 feet; I encountered a severe gust that destabilized the aircraft; causing us to veer significantly right of the centerline with unlevel wings. Consequently; I made the decision to execute a go-around.During the go-around procedure; due to the FO forgetting; I announced a positive rate of climb and instructed the gear up. I then called for FMS NAV; but the first officer mistakenly activated the NAV function rather than L NAV; which caused some confusion. Given his flustered state; I requested he simply provide a heading. He struggled to locate the appropriate button as we continued our climb; and I focused on maintaining the runway heading manually until we reached 1;000 feet; when I asked him to initiate a flight level change to 210; he hit FLCH (Flight Level Change) but still he remained preoccupied with rectifying his earlier mistake with FMS NAV. Taking initiative; I adjusted the speed myself and instructed him to set flaps one; followed by flaps up and execute and after takeoff checklist. At this point; ATC inquired about our status; and since the first officer was not responding; I confirmed that we had executed a go-around due to the gusty winds and unstable landing conditions. They instructed us to climb to 3;000 feet on the runway heading.However; the first officer continued to be flustered; focusing intently on the glareshield buttons and I became distracted in watching what he was doing and what buttons he was pressing. In this confusion; I inadvertently neglected to level off at 3;000 feet and realized we had surpassed the altitude by 300 feet. I promptly corrected our altitude; just as ATC informed us we could climb to 4;000 feet. Unfortunately; the first officer remained flustered for the remainder of the flight.