Yes, you are right. We do sound like the stooges. All anatomy parts of the arm got mixed up :)
Irregardless, I don't think the bruise was caused by her laying down on her arm (although possible). Do you or your uncle pick her up under her arms? If yes, it is possible that slight pressure could have caused her a bruise. Being on Aspirin, even if every other day, thins her blood so she is even more likely to bruise (plus, she is so frail).
Yes, Aspirin should be given to someone who is not mobile to prevent blood clots. If you are giving her 81 mg every other day, that will probably be fine but if you are giving her 1/2 of 81 mg, that will not do anything anyway (that dose has no heart protective benefits and does not thin blood enough to prevent clots) so might as well not give her any. If you are giving her 1/2 of 325 mg, it would probably be good to just switch her to 81 mg every other day or even 81 mg ever day.
I don't like to take medications either and understand people who don't want to. If I can avoid giving someone medicine, I always will but, unfortunately, it is not always feasible. Some people are dependent on medications, others are blessed with great genes :) I hope I will fall into the latter half :)
Try to put an ice pack, not just a cold wash cloth. That will help even more. Just put a towel or a couple of sheets of paper towel under the ice pack. Ice is one of the greatest anti-inflammatories. It always works. People underestimate how useful it is.
If the skin tear is no longer draining, you don't even need to put a bandage on (as long as your aunt will not pick at the skin). Open skin wound will heal quicker with nothing on it. In my personal experience, leaving a bandage on for a day or longer makes the wound even wetter but if that's not your experience, you can definitely leave the band aid on and see what happens.
I will be logging off for the night but will check my email the first thing in the morning in case you write back.
Sorry for this lengthy answers and for getting all confused on the body parts :)