When you take an antibiotic like doxycycline, it will kill off some probiotics. This will completely change the gut flora balance. It can be that something nasty has started to grow, or that just some of the batceria are unbalanced.
If you have probiotic imbalance, some bugs might produce more gas than before, and the increase in gas will slow down the fecal passage.
There are some approaches to change this, depending on what has happened.
a) make a lactulose breath test to make sure no bacteria has moved into your small intestine.
b) take probiotics to refill the missing ones
c) diet change option 1) stay clear from sugars and carbs for a small while. Bacteria love sugars and starch, so not eating this will kill some of them off, mostly the bad ones (the good ones prefer fibre, garlic, etc anyway). At the same time, take a good probiotic.
d) diet change option 2) eat food rich in fibre, that are pre- and probiotics known to change gut flora: Kiwifruit, home made sauerkraut or kimchi, homemade yoghurt and kefir, onions and garlic, lots and lots of garlic.
Welcome to the gastroenterology community! I would recommend you see a GI doctor about this and get some testing done to figure out what is causing this.