Unlikely to get mega ill. Not from mice anyway.
I have unfortunately become an expert in rodents in the last few years. There will not just be 1 mouse. There will possibly be double figures. You need to figure out where they're coming from, traps are great but won't actually solve the issue when the next family rock up. There's a very good chance they're entering your kitchen from the space under your cupboards/sink. If you have a suspended floor, then it'll likely be via that space, or via waste pipe spaces. Have a look around the outside of your house for any gaps in the brickwork/pipes or paving. Fill any gaps in the aggregate around your kitchen internally - we had to push wire wool into gaps in the bricks where the original (now extended) back wall was (and where gas pipes etc fed in) and then spray with expanding foam. If you have an suspicion where they're coming from, you can buy cheap cameras (I recommend Tapo) and set it up to notify you when there's movement. I watched 8 mice get trapped in 4k not long ago.
The reason it's important to find where they're getting in, is more because of rats. Where there's mice, there's often rats. I have finally concluded that I've got rats in my loft aswell as the kitchen - found one stuck in a gap between bricks under the kitchen cupboards last year, up there with one of the most disgusting things I've ever experienced, but hoped it'd been keeping the mice company as a one off. It was not a one off.
Over Xmas I've watched at least 2 rats visiting my loft (don't seem to be living there thank god) carry away 11 packets of poison in 4k. I also watched one of them get winged by a trap last week and since then nothing. Likely there's rotting rats in my cavity walls atm. BUT even if they're dead, bredrens will be back before long because no amount of poison or traps or wire wool is going to remedy the fact that there is very obviously an entry point somewhere in or around my house. From my extensive online manic research, it'll almost certainly be the current or previous (pre extension) waste pipe. Rats and mice use the entire network of wastepipes as a motorway and then as a B road into your home. Rats LOVE climbing cavity walls, especially ones with wall ties. Mice are happy squeezing through impossibly tiny spaces in your ground floor. Both will eat absolutely anything and everything. They'll also eat through the back of your cupboards to get to the food stuff (over 2kg of dried pasta amongst other things last year in my house). My next method will be a one way valve you fit onto the waste pipe outside (the one in the manhole you should have access too on your property).
Basically tldr, you really need to find and fill the entry point ASAP.