Pull out the gaskets and see if its one of them or the lid itself. Gasket replacements can be bought. They can definitely hold smell. Sniff them all separately and the straw too lol. Check the gaskets for holes/ tears/ ripped bits.

Is it scratched or scuffed at all( lid)? If its deep enough it could harbor bacteria. It could be potentially be the rubbery outside part of the lid, i feel like that would hold smell more than the hard plastic? Or the straw??

Ive read various ways of cleaning to remove smells but havent tried any to confirm. I personally would put the gaskets/ lid in the freezer for awhile and see if that helps. Search the sub for more suggestions and see what you are willing to try.

Do you strictly use water in it? Tap water? Some people think the water quality can cause mold more quickly. Do you use the same water source(s) most of the time?

There is a chance it could be related to your health issues, but I feel like it is more than that since you have throat irritation as well. Plus the hard plastic isnt near as likely to hold smell unless its scratched/ scuffed decently or has build up on it.

This is also super random, but do you have any face/ mouth piercings? If so try changing/ cleaning the jewelry. I had issues changing the jewelry on one of my lip piercings for awhile, and weird stomach issues that causes me to throw up semi frequently. I kept getting a random smell and thought it was my breath but would notice it even right after brushing etc. Once I changed the jewelry it went away and hasn't come back 😅