Being angry is not a good thing. [being = gerund noun 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.

- His being late was not a problem. [formal]
- Her being late was not a problem. [formal]

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]   
- They 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.
- Me being silly is very possible.