Coffee affects people differently. For some it make their bowels move, for others it constipates. The coffee alone could be causing the recent trouble, but you may need to look at the broader picture.
For example, unless you are drinking that much coffee because you addicted to it, you are most likely drinking it to energize yourself for work or some other demand. Those stresses themselves contribute to constipation. Are you getting enough sleep? Another threat.
More fiber is not enough to get the stool moving, it can even cause challenges. It needs to be combined with adequate water (warm water is very good) and sufficient oils. I have decreased my constipation by increasing my oil intake to 7 to 10 teaspoons per day (in meals). I use predominantly, cold pressed sesame oil (1-2 tblspns per 10 oz meal), but also use olive, flax, cod liver (with vitamin D, but limit to 1 table spoon per day) and a small amount of coconut oil (the least helpful for me).
Until recently I have had chronic constipation for 30+ years (I am 48 now). For many years it was very common to not have a BM for 3 or more days. I have never used stool softener, laxatives, enemas, or supositories, mostly because I have always been aware that they should only be a temporary fix. Reliance on them comes with it's own set of problems.
I am not where I want to be yet with my BM issues, partly because of other complications, but I constiantly have a healthy BM daily and am beyond the fear of total blockage, because I know what can be done.
I recently began taking an iron supplement (for low iron) and within a couple of day felt things stop moving inside me. I began immediately addressing the issue. I did not have a BM for 3 days, not even the urge. I made sure I was eating very digestible foods (well cooked, soups or stews), consumed the high end of my oils (beyond 10 tblspns per day I break out with skin rashes), Increased my water (all warm), and avoided the things I know constipate me, i.e. beef or pork (I eat mostly chicken or duck instead), refined sugar and bread (both tend to be mucus forming), and I dropped the iron supplement, since I felt certain that was the culprit.
I ate less simply because I was packed full and also because I knew from experience that more liquid and less solid would minimize the danger of impaction.
I also made certain I kept my abdominal area moving, doing everything from twisting and stretching, to massaging and curling (but no ab crunches) constantly through the day. If you like dancing, both the emotion joy and the physical actions have moved my sluggish bowels on numerous occasions (sort of reverses the negative impact of stress and the seriousness of life)
On day 4 I felt the urge (slight) and in one sitting eliminated a couple days worth of stool. A second movement later in the day and I felt I was back to where I should have been prior to the stoppage.
This is my story. I know constipation is a much larger issue with many variations. I would encourage you to gather as much information as possible now to avoid future issues (read some posts from the Ostomies thread on the forum to get an idea of how bad it can get).
I strongly caution you against straining to move things. For many, myself included, it has resulted in hemorhoids, rectal prolapse, pelvic floor disfunction and a host of other serious issues. And I also would again add the cautionary note about relying on the stool softeners, laxatives, etc.
I hope you can see some options for healthy changes here, and I wish you luck on you healing journey.