Yes, it will be safe for you to drink alcohol 48 hours after stopping doxycycline.
In fact you can even drink alcohol while you are taking the doxycycline. The alcohol will not stop antibiotic from working and you shouldn't experience any nasty effects.
Some health professionals will recommend you avoid alcohol whilst you are taking antibiotics for an infection to give your body the best chance possible to fight the infection.
There are certain antibiotics where alcohol must be avoided such as Metronidazole, Tinidazole and Bactrim because the combination may result in a severe reaction.
Drinking any amount of alcohol with these medications can result in side effects such as flushing, headache, nausea and vomiting, and rapid heart rate.
There are no such side effects issues when alcohol is taken with doxycycline.
For a list of antibiotics that have significant interactions with alcohol see the table here: www.drugs.com/article/antibiotics-and-alcohol.html