I have never had a problem with jellyfish in the gulf, only in the bay. You will want to keep an eye open for man-of-war in the gulf though. Take some meat tenderizer along and make a paste out of it and rub it on the stings, if you get stung.
Seaweed should be up. It is always there in the spring and summer. Some of the beaches they drag with front end loaders to clear off the seaweed.
If you are staying at the state park, just give them a call about conditions at the park. 361/749-5246