Generic clarithromycin is not that expensive, is it? Won't be as cheap as chips as PenV is, but cost is not the main issue IMO.
It is a second line antibiotic, useful for atypical bacterial infections as well was garden-variety ones and should therefore only be used if first-line treatment is not appropriate ie allergy.
FWIW, my DS2(9) spat generic Flucloxacillin across my kitchen which made me very cross, right up until I tried it - it's vile, proper gag-inducing horrible.
Most sore throats including tonsillitis don't necessarily need antibiotics btw. as they are self-limiting after 5-7 days. Which is how long it takes for antibiotics to take effect.
So, yes, either give it (bribe, cajole, beg - whatever works) or don't. Clarithromyin is not appropriate, but I know I have compromised my principles when asked, so asking your dr won't hurt...