Short answer: no, don't publish this. If you want to publish anything, you should first make sure you've stated the theorem properly.
As has been discussed in the comments, the theorem was a little unclear. But you've explained what theorem you actually meant, so let's state it once more to avoid any confusion.
Option 1. For any integer $m>4$, there exists a sequence of $m$ consecutive integers such that at least one number in that sequence has at most $2$ distinct prime factors.
This is trivial: I can give you any sequence starting at a prime, for example, $$23,24,\cdots,23+m-1$$ and that is such a sequence (since the first number of the sequence, in this case, $23$, has $\omega(23)=1$).
However, let's state the other two options here.
Option 2. For any integer $m>4$, there exists a sequence of $m$ consecutive integers all having at most $2$ distinct prime factors.
Option 3. For any sequence of $m>4$ consecutive integers, there is a number in that sequence with at most $2$ prime factors.
The third option is disproved by MooS and Patrick Stevens by counterexamples (see MooS's answer or Patrick Stevens' comment).
Option 2 is also disproved by Patrick Stevens, by cleverly noting that any sequence of $30$ consecutive integers contains at least one multiple of $30$, and so at least one number in that sequence has at least $3$ prime factors.