Can I make a Bloody Mary from tomato paste or cooked tomato juice?

I really like the taste of Bloody Mary drinks, but unfortunately I can’t drink more than like 2 sips due to raw tomato intolerance. For some reason, just consuming raw tomato juice immediately induces nausea for me (even after just 1 small sip), and eating cherry tomatoes causes me to immediately throw up.

However, when tomatoes are cooked, I don’t have any problem with eating them. So I can eat tomato-based sauces, ketchup, etc, without any problems. I also don’t have any problems with any other fruit, even those in the nightshade family.

Anyway, can I make a Bloody Mary from cooked tomato juice or tomato paste, or are there alternative fruits to use?