I know what you're talking about - I also have a somewhat sick feeling in such situations, but that's just part of the game. Granted, if the opponent is on a flush draw, he has quite some outs to beat you - but even if he is holding something like 7h8h, you are still way ahead. You of course have a couple of outs for your full house, too.
Moreover, there are numerous other possibilities for the opponents holdings - I think a lot of players would also put all their chips in holding just two pair or an overpair. It could also happen that both opponents are on a flush draw, reducing each others outs.
Anyway, the thing is that in any scenario folding would be a clear -EV move. But you know this. You have to accept losing such a hand despite being way ahead happens. Remember you will be in the same or similar situation a lot of times again, and most of the time you will definitely win. Since in cash games it's all about EV, don't waste money by folding the nuts!
Calling and losing the hand might put you on tilt, right. You might lose more money if you tilt, also true. However, IMO the solution is not to avoid this situation by folding such clear +EV hands and basically throwing money away, but rather to work on the tilt problem itself. Force yourself to stop playing if you lose such a hand. I know this is difficult, especially if the opponent won despite making a very bad call and you think you might get your money back if you continue playing. But you won't if such a beat upsets you too much. So take a break for an hour, a day or how long it takes you to stop thinking about this stupid hand over and over again.
actually i think 78 hearts would
be a favourite in this hand... or atleast not a big underdog....lets count for fun!
4h 9c 6h our friend got 99 no heart.
8 heart outs with 78 (9h is dead as that would give 4 of a kind)
4 fives and 4 tens= ~16% turn 16% river for straight.
and flush adds 16% turn and 16% river aswell.
however some of these is doubles (like 10h 5h) so we got to take them out of the flushdraw. meaning 6 hearts left to hit?
so 6 hearts + 8 straight card possibilities=14 cards times 2 means 28 cards to hit times 2%=56% chanse for 78h to hit his hand. altho! we need to count in the 999s counter chanses to beat a outdraw.
as 6s and 4s would give the other opponents 4 of a kinds he got one 9 left in the deck and the chanse of both the turn and the river pairs with eachother... how to count that out well only way i could think of is to add another 6% on the rivercard to pair with whatever the turn card was. (as its then 3 cards left of that kind thats not in someone whos activly in the hand?) meaning our friend got a 2*2% (the last nine) and a 6% for pairing last card-
shortly 10% of drawing out vs a possible flush/straight.
so the 78 of hearts got at its worste a 56-10% chanse to win ~46% chanse to win?
if my countings are off please correct me im still learning this game..
however the 78 beeing a 46% favourite makes you right he IS a big fabvourite to win this hand as big as 54% favourite if im right.
and id always be ready to gamble if i was even a 51% favourite