Ok, I’m going to quote some old rules of Etiquette here… things that aren’t always followed today, but how these types of situations were handled in the past.
First one engaged… was usually the first one to pick out their Wedding Dates (this was a courtesy you as the second engaged person in the same extended family, should have extended to your cousin)
And if she chose a date within the following 12 months, then the proper thing to do was to go after her date. BUT if she chose a date, longer than 12 months out, then it would have been ok for you to marry within that year’s timeframe… as long as it wasn’t in the same season… (so she chose Fall 2013, you could have chosen Spring or Summer 2013).
This gives a natural break of 3 to 4 months between the Weddings, so that friends and family members common to both of you can sort their financial obligations accordingly… (ie so the last one to be married, doesn’t end up with no one coming, because everyone spent money to go to the other wedding that was just a short time ago)
Now for the last part of your Question.
Some family issues (such as someone going off to War, or Family Illness) take precedent oftentimes as to WHEN a Wedding is scheduled. And because of that many rules of Etiquette go out the window.
If both her Mom & Gramma are ill… then she probably has taken that into consideration in choosing her date.
You should certainly therefore take her choice as not being a slight against you in anyway… and sincerely hope that her much loved family members are there to see her married (to not wish this, or to focus on any other petty item would be cruel at this time under these circumstances that she is facing in addition to planning her wedding, which is supposed to be one of the happiest days of her life)
On the plus side for you, 7 months is a good amount of time between her Wedding and yours, so I don’t think you have anything to worry about… the turn out for yours will no doubt not be affected by her event.
Hope this helps,