I think that there's less of a chance that you've hit the upper file limit, and that it's more likely you have too many files open at once. If possible, I would suggest closing any header files that you aren't modifying on a day-to-day basis.
You may have already tried this, but you might be able to put your cursor over the area where the files are and use the mouse scroll wheel (two-finger swipe if you're on a laptop) to try to see if you can pan through the "tabs" of open files. I don't know if this scroll/swipe gesture works or not because I haven't been in this particular situation before on the OnlineGDB code editor, but I know that it works on most other code mainstream editors.