Seems unique

Say the mystery number is $n$ .

Since $n$ is $3$ more than a prime (and that prime is clearly not $2$ ), $n$ must be even.

Since $n$ is a divisor of itself, and the sum of its divisors is $120$ , we must have $n<120$ .

There are only four even numbers less than $120$ with digit sum $11$ : $38,56,74,92$

It's easy to check that, of these, only $\boxed{56}$ has the correct divisor sum.