It's tricky to manage the pain of rib fractures, and opioids can compound one of the big complications (development of pneumonia) by suppressing your respiratory drive. Multimodal pain control is recommended, typically starting with non-opioid pain relievers, reserving opioids for breakthrough pain. Your options are:
1. Acetaminophen, or Tylenol
2. NSAIDS like ibuprofen
3. Opioids
4. Local nerve blocks
And I'm sure somebody will advocate cannabinoids (CBD stuff), though I have no idea on their use for this indication.
Rather than getting pissed off and determining a priori you'll need more opioids than were offered, I suggest you try to optimize the non-opioid options. Assuming you have neither heart, liver, kidney failure or stomach ulcers, I'd start with scheduled acetaminophen +/- NSAIDS. Something like:
1. Tylenol, 1g three times a day, scheduled.
2. Ibuprofen 400-600mg three to four times a day for breakthrough pain.
3. Lortab for pain than persists despite both of the above. If you take Lortab, you have to be cognizant how much acetaminophen is included (typically 325 mg), as you shouldn't take more than 4 g Tylenol per day. And you shouldn't drink any alcohol.
4. If all that fails, contact you primary care provider and ask for a referral to a pain specialist, as they have several other therapies at their disposal + are more likely to be comfortable using opioids for severe, refractory pain.
Also, make sure you are using an incentive spirometer (device to keep your lungs inflated) and have a cough suppressant handy, as coughing can really exacerbate the pain. While it will take several weeks for the ribs to heal, there's no guarantee severe pain will be present for the duration. Good luck.