Can drinking soda after using teeth whitening products cause gum recession? I drink soda right after I use it or sometimes a hour later

Not likely. Not likely. However, you can set yourself up for some serious decay, as the soda has phosphoric acid in it which will demineralize the tooth and if there is sugar, you will be ripe for decay. Many sodas also have citric acid which will make it even worse. Drink water. Good Luck.
Bad idea. Teeth whitening products remove surface debris, making enamel more porous. Following treatment with sugar/acid containing soda dramatically increases risk of decay. Water is the best post-whitening choice. And don't over-use whitening products; follow package directions.