Many students are confused about when the present participle of a verb (the verb plus –ing) should be called a gerund. So before answering your specific questions, let’s review what a gerund is.
A gerund is a present participle that is used as a noun:
Smoking is bad for your health.
Your driving is terrible.
He enjoys running.
Let's look at the example you gave:
He’s always shouting.
In the above, the present participle “shouting” is being used to form the present progressive tense. It is not being used as a noun, so it cannot be referred to as a gerund in this sentence.
Here’s a sentence where “shouting” is used as a gerund:
Shouting loudly is unnecessary.
Although it acts like a noun, a gerund can take an object and an adverbial modifier (in the last example, the adverb “loudly” modifies "shouting").
Now let’s look at the second verb you’d asked about. The present participle in “I’m wearing” is again forming the present progressive tense and is not a gerund. If we wanted to use "wearing” as a gerund, we could construct a gerund phrase. A gerund phrase is a group of words that is introduced by a gerund. The entire phrase acts like a noun. For example:
Wearing long dresses is inconvenient.
In this sentence, “wearing long dresses” is a gerund phrase. “Wearing” is the gerund, and “dresses” is its object.
Here’s another example:
Smoking cigarettes is bad for your health.
In the above, “smoking” is a gerund, and “cigarettes” is its object.
Now let’s look at your specific questions. You’d asked what was wrong with the sentence "He’s always shouting."
There is, in fact, NOTHING wrong with it. The present progressive tense is most often used to describe actions that are in progress at the time of speaking, but can also be used with adverbs of frequency (most commonly “always” and “constantly”) to describe habitual actions. Usually these are annoying actions of others that we find irritating. Examples:...