Adjective to describe an argument that changed my mind or makes good sense?

Compelling comes to mind.

merriam-webster tells us:

very interesting : able to capture and hold your attention
capable of causing someone to believe or agree
strong and forceful : causing you to feel that you must do something
[...]
He made a compelling argument.

Another option might be persuasive, as Gary's Student mentions in his comment. As merriam-webster defines it:

able to cause people to do or believe something
able to persuade people

Try the adjective cogent if you want to say the argument is logical, well-organized, and persuasive. Wiktionary shows the following senses:

1. Reasonable and convincing; based on evidence.
2. Appealing to the intellect or powers of reasoning.
3. Forcefully persuasive.

If the article helps in choosing one point of view from among several, or if it expresses an argument nearly irrefutably, consider decisive, with its sense “Having the power or quality of deciding a question or controversy; putting an end to contest or controversy; final; conclusive”.

An article that presents its argument neatly and compactly may be called pithy. From en.wiktionary, it means “Concise and meaningful”.

Also consider enlightening, present participle of verb enlighten, which is “To make clear to the intellect or conscience; to shed the light of truth and knowledge upon; to furnish with increase of knowledge; to instruct; as, to enlighten the mind or understanding”.

Influential may also convey the idea:

• having the power to cause changes : having influence

• having or exercising influence or power; "an influential newspaper"; "an influential speech"

  • His theories have become more influential in recent years.
  • My parents have been the most influential people in my life.

Source: www.thefreedictionary.com

Telling

as in, "It was a telling argument."

telling adjective

: producing a strong or important effect

: giving information about someone or something without intending to

Source

I had to add a second one, because it was bothering me that nobody had...

Cogent

1: having power to compel or constrain

2a : appealing forcibly to the mind or reason : convincing

source