The sources linked are great but the tone of this post is such that it really only serves to make people anxious rather than to inform. The least you could do is mention what daily dose is safe (1200 milligrams per day for ibuprofen, preferably not for extended periods) and how often you would have to take ibuprofen on an empty stomach for it to make you start vomiting blood (very, very often).
The risk of destroying your stomach with an NSAID if you use it a few days in a month, and no more than the recommended dosage, is low. Usually, well before you would start vomiting blood, you'd get stomach pains and acid reflux. These can be warning signs that your stomach is sensitive to NSAIDs.
Acetaminophen is one of the greatest drugs we have. We have no painkiller with less side effects than acetaminophen has. It's ridiculously safe compared to other painkillers, even to other drugs. It's so safe that a lot of the reported side effects and deaths are due to other active ingredients (think children taking acetaminophen syrups that also contain propylene glycol, which is a lot more toxic).
It won't destroy your stomach or liver if you know how much to take, and is actually the first choice painkiller in many countries. It is way less harsh on your stomach lining than NSAIDs are, and liver damage is rare and usually only occurs at 150mg/kg a day (so, for someone weiging approx. 145 pounds, that would be around 10.5 grams, when the recommended maximum daily intake is 4 grams). Of course if you take your paracetamol with alcohol, you can damage your liver with less, but you shouldn't (routinely) combine any (pain) medication with alcohol, frankly. Additionally, you should always be cautious if you have had, or are suffering from liver disease.
Recommended maximum dosages are:
Acetaminophen: no more than 3000-4000mg per day
Ibuprofen: no more than 1200-1600mg per day
Naproxen: no more than 500-750mg per day
When taking painkillers, make sure the daily dose is equally spaced over the day. If you get stomach complaints after taking NSAIDs, consider taking them with PPIs to protect your stomach lining (such as omeprazole, esomeprazole, pantoprazole). You can take the listed PPIs once or twice daily, up to 80mg per day. Depending on the country you live in they could be available over the counter or on prescription.
It's important to realise that if you regularly need painkillers, let's say for more than 10 days each month, or more than 5 days at a time, that's worth contacting your doctor about.
If you use acetaminophen and NSAIDs incidentally (with or without PPIs), then they're absolutely safe (if you didn't already have a gastric ulcer, liver problems, you don't take them with (large) amounts of alcohol, or other medication that damages your stomach lining). But if you need them (near) daily, then you should seek medical advice, to make sure you don't destroy your stomach and liver, definitely, but also to figure out if there's an underlying cause.
It's not recommended to use acetaminophen or ibuprofen daily, but I think it's important to realise that there are many people in the world that are prescribed acetaminophen or NSAIDs for (near) daily use, and that many of these people use them for years on end, and they don't all succumb to liver failure or vomiting up their own blood.
The most important thing is being informed. Not scared. Informed.