かえって
on the contrary, instead (it backfired)
かえって + result opposite to the intention
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かえって says an action had the opposite of the intended effect: 手伝ったつもりが、かえって迷惑をかけてしまった, "I meant to help, but I actually made things worse".
The first half is usually an attempt (helping, hurrying, taking medicine, explaining), and the second is a result that backfired: 具合が悪くなった, 時間がかかった, わからなくなった.
It also works for general truths about false economies: 安い物を買うと、かえって高くつく, "buying cheap things ends up costing you more".
Compare むしろ (N3), "rather, if anything", which compares two options. かえって is about expectations being reversed. It's written 却って in kanji, but usually appears in hiragana.
Examples
手伝ったつもりが、かえって迷惑をかけてしまった。
I meant to help, but I actually made things worse.
薬を飲んだら、かえって具合が悪くなった。
I took some medicine, and it actually made me feel worse.
急いだら、かえって時間がかかった。
I hurried, and it ended up taking longer.
安い物を買うと、かえって高くつく。
Buying cheap things ends up costing you more.
説明を聞いて、かえってわからなくなった。
Listening to the explanation only confused me more.