how to make sure what I mail gets there

I've had 2 situations where I mailed something that never got there and they were both important, one was some paperwork to my doctor to fill out so I could get para transit, I mailed it twice and she never got any of it, then when I messaged her online her assistant said to fax it, I found out they gave me the wrong fax number and they faxed it to the right one. I heard it takes a month to process so I'm waiting to get mail from them.
the other one was when I filled out something online from syr housing where I used to live and they called and sent me paperwork, I filled out everything and copied it the same day. this was back in may, I sent them a question online about it and wondered what happened that I never heard back from them, found out they never got the forms I mailed out. someone told me I needed to use their envelopes cause of the code on them, I did use theirs but ran out of room so I used mine too. why didn't the post office ever deliver them, had the right address, they're going to send me the forms to fill out again, how do I make sure they get them , I've thought of asking for their fax number. do libraries fax stuff? how can I send them in such a way that they get them?

Nick1 · 61-69, M

Go to Post Office. Give mail to counter and ask for receipt/ proof of mailing. It will have recipient’s zip code.
Or as Penny said, you can send with return receipt or through registered mail. USPS will charge for those services. Return receipt is least expensive and is acceptable proof in case of dispute.