Using wireshark, you will be able to find out the host name, as mentioned by some other answers, due to SNI. Also, you'll be able to see some parts of certificates. The https URLs you've seen were probably the URLs of CRLs or OCSPs.
If someone could get at your URLs by walking your site, and compare the size of the returned pages with the size of what's returned in your encrypted page, they could make assumptions about which page your program called. But, as you want to put some parameters into the URL and hide those, this isn't a big attack vector in your case. If your URL is
https://my.server/api?user=scott&password=tiger&highscore=12345, and your api always returns pages between 1000 and 1010 bytes, seeing 1007 bytes returned won't help anyone determine user or password or how to enter a highscore.
https is only secure if you prevent MITM attacks. Tools like fiddler, charles or mitmproxy redirect your traffic to themselves, present a faked certificate to the client, decrypt the traffic, log it, re-encrypt it, and send it to the original site.
If your client relies on the OS's truststore, then the attacker will be able to insert his own certificate into the truststore, and your client will not notice anything. The READMEs of the abovementioned tools have instructions how to do this.
So, if you go https to prevent decryption, you will need to check if the certificate returned by the server is correct before you actually send your URL. Check how certificate pinning works for your OS/programming language, and use the above tools to make sure your client will detect a fake certificate and not send the URL before you publish it.