i am sorry that the weaning process was so quick for you, though i would still offer as it may be a temporary strike. aside from that, no i wouldnt introduce the sippy. the first year, breastmilk should be the diet, and the solid food given was just to compliment it and prepare for the future. after a year, solids would be the main diet, ideally with breastmilk complimenting it.
since breastmilk at this time is not an option, milk is what is typically given. but there is actually no need for a child to drink cows milk. you can google that topic and find toms of information. as long as your son is eating well balanced meals, and getting calcium thru yogurt, cheese, ect, he is fine. if weight gain is an issue, you can turn to healthy fats like avocados, but honestly, as long as he doesnt drop drastically in his charts, he would be fine. if he seemed like he wanted something, i would def keep offering the breast at night as its usually the last to go, and maybe pump awhile to try and see if he would prefer the taste of breastmilk in a cup, and also just in case he were to change his mind about night feeding since its usually the last to go. but if it goes, i would say he doesnt want anything at all. good luck, im sorry it was so quick, but you have done an excellent job!!!