Are pets/animals in the cargo hold monitored inflight for any sudden medical condition?
To the best of my knowledge, no modern (i.e. currently used in regular commercial service in statistically significant numbers) commercial passenger aircraft have access from the main passenger cabin to the cargo hold, so there is no way for the cabin/flight-deck crew to check on the critters below, even if they wanted to. My knowledge, however, is incomplete, as was pointed out in the comments, the 747-100 &amp; -200 (and likely the -400) do have access from the passenger cabin to the forward cargo hold. The flight crew were notified when animals were stowed there, however, a long-serving 747 pilot indicated having never checked in on said animals.

Large and/or high-value animals such as elephants, giraffes, etc. are shipped as cargo via specialist transport companies where arrangements to have them tended in flight are common and accounted for (hat tip to Simon). I doubt you'll see someone pulling up to the departures gate at LGA with an elephant in a crate and wheel him up to the curb-side check-in gate.

As a personal anecdote: When I flew from JFK/KJFK to TLV/LLBG in the mid-80s we took our 2 dogs since we were moving there for a period. We got to walk the dogs on the tarmac just before they were loaded in their crates and put in the hold (747, probably -200) at JFK, but there was no mention of anyone checking on them mid-flight. 

Fun fact (for me): We also got to walk the dogs at TLV just prior to our return flight, and that walk ended up taking about an hour as we got to watch them jack up a wheel on a 747 to change a flat tire pre-flight. (Yes, security was much different then. Even in Israel at the height of their occupation of southern Lebanon.)