Could you be a bit more specific about the situation in which you expect to get a comment. In the current revision you write: "I do not get a notification when someone writes a comment under an answer, where I commented too." AFAICT that is exactly how this is supposed to work - with one notable exception that if you and the OP are the only users who have posted comment there. Some references which describe this behavior:
Although the simplest way to describe this is that if the
@username is removed by the system, that is precisely the situation where the user will be notified even without it.
Re: "Also it is a little bit annoying to use @... to make sure your comment gets noticed." OTOH this is a way to ensure that those users for which the comment is relevant will be notified. (If each commentator would get a notification, we would have much fuller inboxes - and after excessive amount of notifications, people are more likely to start ignoring them completely.) I will remind you that you can use autocomplete, i.e. you can type @, the first letter of username and then press tab, to be able to enter the username faster. This feature is called autocomplete. (IIRC this does not work on mobile devices.)
Following posts and SEDE queries
You have also asked: "Are there other methods in checking your own comments, other then going on your profile?"
I will remind you that it is now possible to follow posts - so that you get notifications from them as if you were the OP. But doing so on all posts where you left a comment might be unpractical. (Still, maybe at least on those which are interesting for you, you could use this feature to make sure that you'll be notified about all comments, regardless of using
You might try to use SEDE. (SEDE has the disadvantage that the data is updated once a week, but it is at least something.) Here is a query listing the posts where you have recently commented. And from that you can build in various ways queries listing the recent comments on those posts. For example, here is a query returning recent comments on the posts where you left a comment at some point. (You will see only the comments before the last update - which was on Sunday. Notice that I have restricted this to the comments posted only after some date - otherwise that query took very long time to run. Again, maybe somebody more experienced with SQL would be able to improve the query so that it is more efficient and runs faster. When I tried the same query on meta, I was able to use a longer time interval - most likely because you have less comments on meta and there are less posts to check.)
I thought that maybe something like this might be possible also with Stack Exchange API. I have asked some more experienced users in chat - the response seems to be that this probably would not be feasible.