I know I have to start the sentence with 「最近」for "lately" but I don't know what to say for the rest of the sentence. Could someone help me with this?
Does it go like 「最近私は面倒くさい人です。」?
Also,
I agree with Naruto's comment that saying "I have been an annoying person lately" in a formal setting to someone like a boss seems a bit strange. However, if there is a situation where the speaker is on very good (close) terms with the boss/teacher person, then it may be possible to say a phrase like this, but only if it in the context of apologizing or explaining for reason for that behavior.
Assuming that, here is my guess at a Japanese phrase to express what you want.
私は最近、周りの人に迷惑をかけていると思いますが、。。。
This literally means something like "Lately, think I have been being a burden to those around me, but ..."
The sentence could continue with something like "これからは” (going forward) to explain how that person is going to change.
Another word that could be used to be mean "annoying" is "うざい” but this is a pretty rough word I have only heard in familiar conversation.
I think a problem with your question is that it comes from a very Westernized cultural point of view. I don't know the exact situation with your senior, but Japanese people don't like to publicly speak openly about negative feelings and blame, so more often they thank people. Therefore personally I would say something like,
最近はいつも助けてくれて本当にありがとうございます。
Thank you so much for always saving/helping me recently.
Of course, as I don't know your situation this might not be true, it depends on why you've been annoying and your relationship with them. You can always change the verb to something more appropriate.
As to the translation you made, I think if you said this to most Japanese people you would make them feel uncomfortable (a big no-no in Japanese society). This is because you are saying very negative things about yourself and they would feel the need to tell you not to worry, etc, so it sounds like you are fishing for compliments. Further, you are not directing your nuisance towards someone, but giving yourself a general negative trait (lit: I am an annoying person).
The phrase for being a nuisance to someone in Japanese is 迷惑をかける, so you could use this in te form with an apology. However, culturally Japanese people expect actions to make amends, so I would definitely follow it up with some sort of plan on how you won't be a nuisance in the future (これから...頑張ります。). If your senior is really Japanese though, you would probably want to stick with the first idea of thanking them.
