The treatment for PEs/DVT (blood clots in the legs or lungs) is warfarin - typically for 6 months or longer depending on individual circumstances. Aspirin is not used for treating pulmonary blood clots. As you having a long history of DM you may benefit from taking aspirin for other reasons (prevention of heart attacks/strokes) although the evidence for aspirin in primary prevention (i.e. people without overt evidence of cardiovascular disease) is not particularly strong. Aspirin is not generally given with warfarin so if you were to take it you are probably best to wait until you stop your warfarin.