Welcome to the gastroenterology community! I don't think this is necessarily caused by tasting the starter and I would recommend you see your doctor about this.
Have you tried any new foods/foods that you normally do not eat? Do you work with/handle a lot of gluten products?
More than likely you probably just ate something that (obviously) did not agree with your digestive system. Try some Gas-X to help with the gas and bloating... I am lactose intolerant and it has helped me out before.
I am not sure about going to see a doctor... unless this problem has persisted since four days ago. If it just started give it 24-hours to run its course. I really would not be too concerned, but rather consider yourself lucky, if this is your first time experiencing smelly gas/stool. :) There is no harm in calling your doctor though and asking if they would recommend anything. Please keep us updated though.... and if your symptoms do persist/get worse I would contact your doctor again, if what they recommend does not help.
Ah, I should have clarified- this has been going on since the morning after I ate the starter. At this point it's been five days and no change, still having truly foul gas and stools (which are now quite infrequent, orangeish, and very thin, if that has any relevance).
It may be that something unrelated to the sourdough starter is bothering your system. I wouldn't really know for sure what is bothering your system, but orange stool should never happen and is obviously a warning sign. I'm not sure what warning sign it is, but it obviously can't be good. Usually greenish stool has something to do with the gallbladder, but I'm not sure what orange stool means. It can't be good, though.
Also, the one one thing to definitely avoid while on a vegetarian diet is all those soy products. Many vegetarians become violently sick from all that soy being used to get protein. Soy is NOT health food and the majority of it, including tofu, is NOT properly fermented in the traditional way. These soy products that are on the market mimic estrogen in your body. People have become highly allergic to soy after consuming so much of it on a vegetarian diet and have almost died from it. This is not an anti-vegetarian post, so don't take it that way. Soy is known to cause a lot of serious and even life-threatening health issues. Please, for your own sake, run as far away as you can from soy.
Please check out this link, it might be very helpful.
Orange poop could be attributed to your vegetarian diet and eating a lot of beta carotene.