Ah I took too long typing! BarbarianMum has it :)
OP you need to make sure your baby is in the shade now, just in case. It’s not the big scary one, but, because of the way the whole plant family works, you need to stop thinking of the plant as the source of risk now, and think of the sun as the source of the risk... the harm comes from the plants making the skin more vulnerable to the suns rays, so the burns come from the sun, not the plant itself.
It’s highly unlikely there’s any harm been done, but just in case, do make sure your baby is out of the sun now for the rest of the day at least.
Also, wipes are better than nothing, but pouring water over the site is best as any toxins will get washed away from the skin.
Having said all that, I do think your baby is probably fine, so try not to panic too much!