Concern about what I am going to face in America

I almost finished applying for a few graduate schools in the US and until next August I barely have specific things do to, so if I spend the rest of time effectively by doing something meaningful, my life there could differ a lot. 

I am seriously concerned with my English proficiency since I am clearly aware that what is going to happen to me while studying in the US. Many native English-speaking friends tell me that my English level is pretty high for not staying abroad and not getting any private tutoring. But it does not sound good to me because it definitely delivers an important message that they feel some awkwardness from my English. When someone cannot feel any accent or difference in constructing sentences compared to ours, we would not praise for their language skills. 

I am specialized in engineering, so that I would not spend as much time in debating with peers as business, economics, psychology majors that strictly require a native-level target language skills even to non-native speakers. But the lack of English proficiency would definitely get in the way of learning things as fast as other natives. Plus I am thinking of settling down in the US after completion of graduate studies, and probably moving country to country where English is exclusively spoken. What's most important is that I don't want to become like other Korean Professors who have studied in the US for almost a decade but still have basic levels of colloquial skills. I am not imagining my English level to reach  native-like fluency in less than one or two years, but I could reach that level sooner than I expect, 5 years, it would be icing on the cake.

Until August, when I start a new semester if I get accepted(I am pretty sure they would pick me), I have around 7 months left. I watched a documentary about during the Second World War young american soldiers over 20 getting extensive training on their French, German 20 hours a day for 6 months before being sent to Germany and France. It turned out that they became fluent in the target languages. I would not be able to study that long hours a day, but it hinted at the possibility of boosting up my English skills as long as I am determined. 

My problem is that I have skipped solidifying my intermediate English level by studying high-intermediate/advanced levels for ESL learners, which means that because of my boasted ego I chose native-like levels of input immediately from a far less level. This is why my learning pace has been extremely slow and I have not made much improvement on my English. I was lying to myself. From now on, I should read/watch/listen to materials with comprehensible levels, understanding at least 80% of input, and from time to time challenge myself with a bit higher levels. Bring it on.