The drowsy/alert effect varies from person to person but it won't affect the antihistamines itself.
I am addicted to Diet Dr Pepper which is full of caffiene (yes I knowh ow unhealthy this drink is for me) and I take them. I still get drowsy. In fact, they lay me straight out. So I don't think its going to hurt you. However, if you are in need of antihistamine, water is a good idea because it thins out mucous and helps you breath and which chest congestion and coughing.
Definitely drink more water, because both the antihistamine and tea and coffee will cause dehydration unless more water is drunk to replace the fluids. And, actually, it isn't the caffeine that is so bad about the diet soft drink, it's the artificial chemical sweetener that is so bad. That's a lot like drinking rat poison in small enough amount you might not notice unless you're particularly sensitive to the stuff like I am. It's actually worse for you than the high fructose corn syrup or the cane sugar either one. Anyway, you are likely so addicted to it not because of the caffeine but because of the chemical artificial sweetener. That stuff truly is more addictive than caffeine is. Not that an overabundance of any form of sugar is so great for you, but the artificial stuff is worse for you. Again, the caffeine itself isn't too terrible for you and it won't cancel the effects of the antihistamine. I often have to drink coffee if I take Benadryl or Zyrtec, just so I will be able to stay awake.
Drinking caffeine in moderation is still key. Too much caffeine is still bad for your health. People who have migraines have to apply a balancing act and can only have occasional cups of coffee or other caffeine drinks, because drinking it all the time can actually cause migraines or make the caffeine ineffective as a means to treat migraines. Drinking it only on occasion can actually be helpful for treating migraines.
There is NO contraindications for drinking tea and taking an antihistimine. It is ok.