I would make it clear you need someone to design this for you. If you want someone to print for you, expect to pay. Be clear about timelines too.

Does your school have an engineering or design department? That would be a possible route to get designs printed. If this is for a project with a deadline, you could coordinate with one of those departments and maybe arrange a joint project. They do the design parts and you handle logistics and concepts.

I'd be interested in fiddling with this but don't want to commit to anything. I'm a hobbiest and could use the CAD practice.

Open fusion360. Make a sketch of a two circles that’re the outside and inside diameters of your replacement cap. Extrude the od to the height of your replacement cap and extrude the id to the height minus the top thickness using the remove material radio button. Create a spiral using the thread tools with a triangular profile and an od equal to your cap id. Measure the threading and tpi of the bottle and input those on your spiral. Merge the spiral and cap into one body.

Make another sketch on the plane that’s the top of the cap. Draw a 1-2mm thick plus or asterisk in the center of the lid extending to a mm away from the id of the mouth of the bottle. Extrude removing material to make a cutout.

Print your test examples in whatever’s appropriate for medical use, but once you have a working prototype, use the flexible material for the top layer.

Gl.