私は次から次へとやっかいなことがある。

English Translation

I am having trouble with one thing after another.

The subject and the verb don’t match and the collocation sounds very unnatural. It can be even interpreted as “I AM a serious troublemaker” (and I annoy others). I would propose:

次から次へと厄介なことが降りかかってくる。(やっかいなことがふりかかってくる)

I (私) is omitted and it sounds more natural. 降りかかる is a compound verb: 降る (something to drop on one’s head) + 掛かる or かかる (something to jump onto one’s body/mind). So. the subject of 降りかかる is often something bad to you.