This question is regarding my own website that I own! I am the webmaster for it, and I am asking this question specifically regarding the web property that I own.
I frequently submit urls using the submit url method here: https://www.google.com/webmasters/tools/submit-url
I have noticed that when I submit urls that need to be re-crawled, they do not get indexed. I frequently submit urls that I do not own here, so would submitting urls that I do not own effect the ability to submit urls that I do own?
Unless you are effectively spamming Google with 1000's of submissions then there would be no reason to receive some kind of penalty that would effect your own site submissions.
However, for your own sites you should really be using the Fetch as Google tool within GSC - which is built for this purpose and allows you to more closely monitor your index status.
I have noticed that when I submit urls that need to be re-crawled, they do not get indexed.
As @closetnoc has already pointed out in comments, there are no guarantees that submitting a URL for indexing will result in that URL being indexed and returned in the SERPs. Crawling and indexing are two separate things.