Being angry is not a good thing. [being angry = gerund nounclause and the subject of the sentence].
To apply this to yourself, use my or me, not I. See the explanation below.
My being angry is not a good thing. [same thing, except it refers to you; formal]
Me being angry is not a good thing. [same thing, refers to you, informal]
Use possessive adjectives for formal constructions, use possessive pronouns for informal ones.
My, your, his/her/its their, our, your = formal
Me, you, he/she/it them, us, you = Informal
DIFFERENCE (another example):
- Their being late was not a problem. [formal]
- Them being late was not a problem [informal]
Being is a noun (gerund) in all those cases. It is not a participle, except in form but not in function.
Being rich is great!
My being late is not likely. [formal]
Me being silly is very possible. [informal]
Being a clueless downvoter is not a good thing.
Being human is complicated.
Playing is a good thing.
Your playing at the concert is not a good idea.
Please note: any verb in English, just about, can be made into a noun gerund.