Behold, the main reason it's incredibly difficult to fit in Jim's upgraded trumpet. While the trumpet is a significant upside, in exchange for it you have to handle this downside - something that might blast you for up to a total of 10 damage and horror. And you'll have to plan for the full 10 - the upgraded trumpet heavily slants you towards wanting curses, so even if you fill the bag with 10 blesses and curses, you're well within the realm of possibility of hitting all of them.

There are two primary ways of dealing with this if you can't completely negate the card. First, you can run plenty of soak. Spare allies wouldn't hurt. Idol of Xanatos is another method of storing some extra health in an alternate mechanism. If you're using the standard back, Obsidian Bracelet can soak a lot of damage from a treachery in one go. And once you have a little more experience, Grounded (3) also remains a generally useful bit of soak and bonus for any spell-focused character.

Second, you can try to heal it after the fact. More effects exist in modern times to burst heal or top off and keep yourself under the threshold. Hallowed Chalice remains a good option without experience, and Spirit of Humanity fulfills a good mixture of roles for you. Jim's Trumpet will also help keep the horror side of things handled. It's also a luxury, but this is one of those cases where I also wouldn't discount Rite of Equilibrium - the requirements for Jim's ability and unique cards here means you might find an eventual use for it.

There are probably more complicated means of mitigating the weakness as well by removing it completely - Jim technically has access to some stacking shenanigans involving Scroll of Secrets/Alyssa Graham and Foresight, but those are more complex abilities. Just be sure it's worth it - there's only so much value you can milk from Jim's Trumpet to try to make it worth all of this trouble.

(I personally recommend Soul Sanctification if you're going to need to have that much excess random team healing anyways.)