Right. So local, not general.
No, that's regional with a lasting national impact. Therefore, being more of a single state issue, it is constitutional. Hell, if it was just New Orleans alone, shutting down the Mississippi river to ocean-going trade, it would still be a national issue due to the economic impact upon the nation.
General welfare means national welfare. If something is threatening our national economy, then it falls under the general welfare.
The only way it wouldn't would be if the storm wiped out an area in Texas which was not heavily populated, did not have any form of major commerce, nor interrupted the national flow of business and defense. In that case, state, local, and private groups would take the burden of rebuilding, and not the federal.