I would like to search for my username user122424 and a specific word used in comments that I remember from reading that comment to get back to it. How can I do that?
Stack Exchange API have a function to return replies to specific user, so it is possible that you could somehow search among replies to you using this. But as I am not really familiar with using the API, I won't be able to suggest details of such method.
As mentioned in the comments, you could use the SEDE (Data Explorer). This was suggested also in older similar posts on this meta such as: Searching comments or How to browse or search comments?. You can also check some posts on Meta Stack Exchange, such as: How can I search for specific comments? pr Can I search my comments using some keyword(s)? (There are also a few feature requests about this: Ability to search comments would be useful or Add Ability To Search Comments Only. So if you think this would be a useful improvement, you can upvote those.)
Most likely interpretation of your question is that your looking for the words which contain both your username and also a phrase you're searching for. I will also include some other queries. Don't forget to switch to the site where you want to search (all linked queries are for the main site here on Mathematics). You can change the parameters to look for different phrases. (Parameters can be changed directly in the url or in the boxes below the query.)
- You can search for comments containing two different strings, such as 122424 and how. Notice that the query is case sensitive. Here is case insensitive version.
- You can also search for comments by a specific user containing the given string. Again, here is also a case insensitive version. (One of the parameters here is the userid of the user whose comments you want to see. Just in case, I'll include links to Help with what is my user id and how do I check it? and What is my user ID?)
- And one more query for comments containing the given word which were made under a post posted by a given user. (So in this case the userid is for the user who made the post, not the one of the commenter.) And here is a similar query, restricted just to the questions.
- Query searching for combination of the given two words only under posts by a specific user.
Maybe it is worth pointing out that the queries search for a given string which might be a part of a longer word. But you can include also a space as a part of the string you're searching for - so this might help in situation when matches for substring/superstring would cause a problem.
And I will include the usual caveat that the data in SEDE are only updated once a week.
Of course, you can create many other queries - limited basically just by the available data and possibilities of SQL. You can find several examples of such queries in the linked posts.