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I use the following sentence construction a lot.
I'm not sure if this is right.
I was not aware of any problem until recently I noticed that quite a few of my colleagues used it a little differently. It went like:
I'm not sure this is right.
Now I'm confused. On the one hand, they are native speakers and might be correct on the usage. On the other hand, my education background convinces me that mine is correct too.
Which one should I use?
This isn't a question of right vs. wrong. Rather, you are describing style differences. The sentence "I'm not sure this is right" is elliptical, meaning it leaves out words that have a grammatical function in the sentence but are implied.
The word "that" is often omitted.
In regards to your use of "if." This word is informally used to indicate options. The more formal word to use here is "whether," as in "I'm not sure whether this is right." However, that sentence, too, is elliptical. The full sentence, with the implied words in place, is "I'm not sure whether or not this is right."
Leaving out the implied words is not incorrect. As I said, it's a style choice. If a sentence is clear without the implied words, and if the sentence has an appropriate level of formality according to the purpose and audience, leaving out the implied words is generally acceptable.
Many native speakers omit certain words when they speak, especially when it doesn't affect the meaning (or the grammar) of the utterance. Your example is one of those cases. So, to answer your question, both usages are correct; the second one is more informal.
