「周りの人に迷惑をかける」は
to be a hindrance to others（他の人の足手まといになる：邪魔になる）
to place a burden on others（他の人の負担となる・〜に負担をかける）
のように言えます。
例：
I was a hindrance to the people I work with because I got sick suddenly and had to miss several days of work.
「急に病気になり数日仕事を休まなければいけなかったので、職場の人の足手まといになってしまった。」
「急病になる」は get sick suddenly と言えます。
miss several days of work で「仕事を数日休む」
I placed a burden on my co-workers when I was absent due to an unexpected illness.
「予期せぬ病気で休んだ時に、同僚に負担をかけてしまった。」
absent で「欠勤の」
unexpected illness で「思いがけない病気」
burden で「負担」
ご参考まで！
周りの人に迷惑をかける - to cause problems for other people
急病で会社を休まなくてはいけなくなり、周りの人に迷惑をかけた - I suddenly became ill and had to take some time off work, which ended up causing problems for my colleagues.
colleague(s) - 同僚 、一緒に働いている人
どんな迷惑をかけたのかを明確に言うともっと英語らしくなると思います。例えば、
I suddenly became ill and had to take the day off work and my colleagues ended up having to do (all) my work for me. もしくは I suddenly became ill and had to take a couple days off work and because of that everyone had to do overtime etc.
カナダ 
イギリス 
