Hi there- thanks for reaching out and sorry about the trouble!
There isn't actually a way to manually index backlinks I'm afraid.
If some of your links aren't appearing, this is definitely due to the way we collect this information for our link index and it is actually expected that we won’t find every page and link because we aren’t looking for them all! When we collect this data, we’re looking specifically for the most valuable links and, rather than crawling your entire site or every site, we collect this by starting our crawler on a few highest ranking sites and letting it perform a breadth first search to see what it finds.
For each page that we crawl, we first collect each of it’s links before following these and collecting the details of each page that these link to and so on. There’s a set limit of links that we’ll crawl per page and pages that we’ll crawl per site so it’s expected that we may not follow every link on a site this way - so we won't always find all your available backlinks.
Generally, we recommend using a wide variety of backlink tools to get the most illustrative picture of how your site's backlink profile looks. OSE and Ahrefs index differently and have different purposes. Ahrefs is good for quantity while OSE is great for finding higher quality links. Domain Authority is our own proprietary metric that is closely correlated to Google rankings, so our customers often use OSE to research influential sites to build links.
I hope this helps - let me know if you have any further questions!