Sure it can, but lots of people suffer anxiety and stress without these symptoms. Even people with anxiety can suffer problems from poor eating habits. Your focus on farts is odd, as they can also indicate digestion problems. What's your daily eating like? Also, when did you start Prozac? Antidepressants cause digestive problems in a lot of people; it's a common side effect, partly because they interact adversely with magnesium.
Absolutely 100% yes, and it's supported by masses of evidence. Look on youtube for a documentary called Stress, portrait of a killer, it contains a lot of work by Dr Robert Sapolsky who is a world authority on the effects of chronic stress (at the risk of being patronising but people confuse them all the time: clinically speaking chronic means lasting or likely to last six months or more or twelve months or more - depending on the specific condition - and acute simply means severe; e.g., I have hypermobility syndrome, which is a chronic acute pain condition...). The documentary also details The Whitehall Study, one of the most significant long term studies on the effects of stress which revealed, among many other invaluable insights, that chronic stress can cause people to gain weight in very specific localised parts of the body, especially around the abdomen; and work conducted by a Californian researcher showed that chronic stress can frazzle your dna and literally kill you by shortening your life, It's extremely serious and something we've heard about for decades but which all too many people are simply not paying appropriate attention to. Although it could also be that you have something else wrong so I would strongly urge you to see your doctor.