How can I stop my family from pressuring me to drink?

At any social gathering - Christmas, New Years, Birthdays etc, my grandmother (and aunt, sometimes) always pressure me to drink wine or champagne. It's not that I want to be a party pooper, but I just don't enjoy the flavour or how it makes me feel. Even a sip seems to make my stomach ache, and the taste makes me feel ill - it probably doesn't help that my mom (who I rarely see and doesn't attend these events) is an alcoholic.

Obviously I recover quickly and it's not the end of the world, but I resent being pressured to drink when I really have no desire to.

I have tried politely declining, saying I don't like it, but it doesn't work. It will typically go down like this:

Them: "Do you want some champagne?"

Me: "No thanks, I'm good with my water."

Them: "Just have a little bit!"

Me: "No, really, I'm good, I don't like champagne."

Them: "Well, if you have some, you'll learn to like it. Just have a sip when we toast."

Me: "Thanks anyway, but it would be wasted on me! I'll toast with my water."

Them: "Here just have a sip and I'll drink the rest after."

Me: "No thank you, I don't want any."

Them: "Oh common, it's my birthday, just have a little! Don't ruin the toast, just have a little."

All this while having a glass pushed towards me. Last time I got so irritated that I dumped out the champagne onto the grass after 5 minutes of this back-and-forth, and was told angrilly by others not to waste it.

I really don't want to be a crank, so is there something magical I can say that will cause them to stop asking me right away without them thinking I'm ruining their evening or insulting their champagne? I would like them to respect my wishes.