In the sentence "I can't stop thinking about you" is
thinking a verb or a gerund? I'm a little bit confused, because there is already one verb
I can't stop thinking about you.
"Stop" is called a catenative verb, and the non-finite clause "thinking about you" is a catenative complement headed by the gerund-participle verb "thinking".
The term 'catenative' is derived from the Latin word for "chain", and is used to describe clauses where two or more verbs occur consecutively, as "stop" and "thinking" do in your example.
Words for actions
It's a gerund.
Thinking is being used as a noun. It's the object of the verb stop. It's like the nouns after stop in these sentences:
You can't stop progress.
I can't stop the celebration now. The musicians are already playing and everyone is already dancing.
Not even the governor can stop the execution now.
Each of these examples uses a noun to refer to an action now in progress, just like thinking.
Adding -ing can also make a verb into a kind of adjective, called a present participle. Here are two examples of thinking as a present participle:
You can't stop a thinking person.
Someday, the human race will be destroyed by thinking machines.
Don't get hung up on terminology
There are some special conventions for using the -ing form of verbs in this kind of context, though. Without an article, the gerund gets modified by adverbs, like a verb, and the subject of stop is normally understood to be the subject of the gerund:
I can't stop bleeding. [I am bleeding and I can't stop.]
I can't stop financially bleeding. [I'm losing money and I can't stop.]
Because of this sort of convention, some people prefer to say that thinking is part of the verb or that it's both a gerund and a participle or that your question is meaningless. (That's why your question got some strange comments.) I think you shouldn't get hung up on terminology. If you know what modifies what, and what are the conventions for implied subjects and which kind of modifier to use, you'll be fine.
Adding an article, or treating the gerund as a mass noun, makes it feel more like an ordinary noun, so it gets modified by adjectives and no longer adopts the subject of stop:
I can't stop the bleeding. [Maybe I am bleeding, maybe someone else is bleeding. The sentence doesn't imply either.]
I can't stop the financial bleeding. [Here you use the adjective financial instead of the adverb financially.]
I can't stop thinking about you. Thinking about you will happen all over the world as long as you are famous.
The last example is strange, but it illustrates the principle.
Thinking is not a verb, at least not in the strict sense of "verb" that contrasts with "gerund". It can't make an assertion:
I thinking about you right now.
This is what the continuous present tense looks like:
I am thinking about you right now.