There do exist red food dyes that are specifically labeled vegan, and thus aren't insect-derived. Wilton also makes a 'no-taste red', which isn't as foul as the normal red color. I've personally found that the red liquid dyes tend to be less obnoxious than the gel-based ones, but I have no idea if other people feel that way, or if it holds true for all liquid dyes (and come to think of it, I was baking cookies with the liquid, while I use gels and powders for icing).
... but I have no idea if these might be available in your area or not. I'd try looking for a cake supply store, or even a bakery that makes cakes and see if they'll sell you some of their supply.
(and I personally was one of those with an extreme reaction to red food coloring (not sure if it's allergies or not) ... so I'm a bit sensitive to the subject.)
If you can't find prepared dyes specifically, I'd look into fruit ... you might not get as bright of a red, but pureed red fruit (strawberries, raspberries, cherries) might get you towards a red shade. If you're not in an area that gets the flown in shipments from the southern hemisphere (and thus out of season fruits), many large grocery stores sell frozen berries.