No, Only Swift Swim + Drizzle on the same team is banned, Sand Stream + Sand Rush/Drought + Chlorophyll on the same team are perfectly legal in OU. Seeing as all of the weather starters are in OU, this does not apply to lower tiers.
•Banned Pokemon - A team cannot have any of the Pokemon found in the following tiers: Ubers.
•Drizzle + Swift Swim - Using both a Pokemon with Drizzle and a Pokemon with Swift Swim on the same team is banned. - Smogon
No where does it say that those cominations are banned.