Help getting rid of a flea problem

Earlier this month I noticed a flea on my dog. I did a flea combing and found a few more on him, so I reapplied his flea meds since he was due for it anyway. I’ve been vacuuming and washing our bedding too. A few days ago I was still finding the occasional fleas and eggs on him during the combings so I gave him a bath. Today I noticed he was scratching a lot so I went to comb him again and I found so many fleas, way more than the first time, probably over 20. It seems like it’s gotten worse. I’m going to call the vet to get a prescription flea med ASAP but I’m really worried about an infestation. My dog is supposed to go to the sitter in a few weeks while I travel abroad to visit family. From what I’ve been reading a few weeks doesn’t sound like nearly enough time to get rid of a flea infestation. I also have a physical disability that makes the constant vacuuming very difficult. I’ve heard of sprinkling borax or diatomaceous earth but I’m hesitant because my dog likes to lick his paws and I’m worried about him ingesting any residual powder after vacuuming. This is the one time of year I get to visit my family and I’m so worried I’ll have to cancel my trip because he won’t be able to go to the sitter. I’m panicking and I don’t know what to do, I’m at a total loss 🙁