I am sorry, but the question does not make sense.
One cannot say that a parameter or some
aggregated data are by itself "statistically significant".
You have to specify a comparison for the working
hypothesis first, such as "the means of the 2 status
groups are the same [in the population]" or "the
correlation coefficient is zero [in the population]"
or "the proportion of black-haired people is higher
than the proportion of people with other hair
colours". So, which comparison(s) do you want
to make here?
It's kind of difficult for me to properly use statistics language because of my medical education. I have recently studied only the basics, but usually I recognize type/way of testing hypothesis (frequencies chi xtest, paired group t test etc.). Is there any chance to simply use these numbers in formula for any specific test or we need more data? Maybe "statistically significant" was bad choice of words.
I agree with all previous comments... there is no proper answer to an undefined question. In any case, since you have count data and 3 different situations (allergy, suspected, no-allergy), a chi-squared should provide you an answer (although, as mentioned in previous answers, the small sample size compromises any reached conclusion)