What could be causing my toddler's health issues?

For almost 2 months my 2 year old has suffered with a cough. It started out as a cold. It lasted more than 2 weeks so his doctor gave him antibiotics because they thought it might be a sinus infection. After a couple more weeks of still being sick he ended up in the hospital hooked up to an IV for dehydration. They also gave him more antibiotics in his IV and did some blood work that showed an infection. The hospital didn’t know where the infection was but said it didn’t matter because the medicine would clear it up anyway. 2 months later he’s still suffering with this cough at night. We took him back to another doctor who claimed it was allergies and prescribed a nasal spray. He’s been taking that for 2 weeks and still no improvement. He hasn’t had a full night of sleep in months and it’s really effecting us all. He wakes up at least 3 times a night in a coughing fit. We give him water. We have him propped up while he sleeps. We have a cool mist humidifier running. We have done everything the doctors have suggested. What could this cough be? Every doctor has said something different and none of the medicines have cleared it up. I’m not sure what I can do at this point but he’s not healthy and I feel completely helpless. Could this be allergies? Asthma? A cold still lingering?