Cessna 172 student pilot reported a low altitude upset and loss of control following a wake turbulence encounter on approach to BFI.

Narrative

I was practicing landings in the pattern. Overall; the pattern was a bit congested and I was considering calling it for the day; after a few laps before and after a flow change. Tower told a few planes to go around to make room for larger planes crossing the runways on the ground; and I waiting on the ground a while longer while waiting for clearance to take off and enter the pattern. Flight was routine up until the incident. While in the downwind for 32R at Boeing Field; I was contacted by Tower and recall being told 'caution wake turbulence' as I was given clearance for touch and go. I believe I acknowledged their warning and continued with my approach to land. Approach was stable and flaps were at 30. I had just reached the point in my landing flow where the runway was assured and pulled back my power to come down and hit my touchdown point when the plane began to yaw to the left and rudder ceased to be effective to counter the motion. I initiated a go-around immediately. I went full throttle and pitched up for Vx to stop the descent; but due to the confusing yaw to the left; this meant that I was going to encroach over the larger runway (32L). I tried to compensate for that with right aileron and rudder; but the input suddenly responded with extreme sensitivity; causing me to roll to a nearly 45 degree angle and for my pitch to drop. I was very focused on keeping my airspeed up; so I let it dip for a split second and glanced at my airspeed indicating just over 65 knots as I tried to roll wings back to level. At this point; I was viewing mostly the grass strip between runways in my windshield and feeling extreme turbulence while full throttle. Luckily; I had ascended slightly when I was previously skewed to the left. In response to the alarming sight picture; I pulled power back a touch; so as not to go full throttle into the ground; as I tried rolling back to level. Response seemed sluggish and unstable rolling back to the left. Once I was back to a turbulent wings level; I quickly but carefully brought my pitch up to level and throttle back to full; with the intention to at least break my descent and build up airspeed that I thought I had lost. I felt my controls responding normally; glanced at airspeed around 63 and building so I kept my power setting at max and gradually but firmly re-initiated a climbing left turn to reorient myself back in line with my own runway. I don't recall my exact altitude since I was mostly focused on the vertical speed indicator and airspeed indicator. Once it was stable at a 500 foot per minute ascent rate; I started reducing flaps and continuing with a gradual ascent into Vx. I do not believe my speed ever dropped below 60 knots; as airspeed was my primary concern as soon as controls stopped responding as expected. It felt like the initial wind push happened very fast and the recovery was sluggish and turbulent. Control responses were very confusing to the point where I thought something had broken on the plane. I felt embarrassment more than fear; in the moment; thinking that I did something wrong and caused a dangerous condition. I didn't know what to say on the radio; so I just listened. I heard other planes going around and I heard Tower report winds coming from 180; so I assumed it was a rogue gust of wind. Once in the downwind; I reported hitting wind shear; but Tower responded with an implication that it was likely wake turbulence. I told them it was hard for me to tell if that was what I hit or not. I made my next landing a full stop; wondering if anybody saw what I had experienced and also wondering if I was going to get in trouble for something I must have done wrong. The Ground Controller congratulated me for an excellent recovery; which made me feel some relief. I forget who was marshaling me in; but they said they saw the whole thing from the ground. A CFI that had been in the plane behind me came over as soon as he could and told me he had seenthe whole thing. He implored me to write a report and told me it was absolutely wake turbulence that I had hit. He told me that when we are in the north flow; big jets often take off around A7 or A8; right where 32R starts. This wake turbulence often lingers for a while; so awareness of the phenomena; ample spacing; and cautious go-around decisions are a must. I thanked him for his quick lesson and told him I would write up the report.Having thought on this incident for a day; I realize just how dangerous a cavalier attitude towards wake turbulence warnings and avoidance procedures can be at this spot on the airstrip. Large planes really do lift off the ground on 32L right where smaller planes land on 32R; or slightly after. I feel that this experience will make me a better pilot and I will be more aware of the hazards that the parallel runway poses to my smaller aircraft. I see more go-arounds and extended downwind requests in my future. Tower does a good job of warning everybody about wake turbulence; but I think pilots like myself have become complacent about the warnings; especially when we hear them so often and incidents like this one are so rare. Wake turbulence is no joke and the hazards are especially present at this airport; and especially when in a north flow.