Okay, I will be quiet no longer
Have you considered getting career counseling and trying to identify other areas that use your talents that might have a better hire ratio?
I have spent the last 4 months in a course teaching counselors the how's and why's of career counseling.
From this vantage point, I see a lot of benefit in broadening your areas of interest, although it is obvious that you are open to anything.
Also from this vantage point, I can see no better time to get more education. I know that you mentioned that you were busy 80 hours per week while you schooled, but have you considered that it does not have to be the same experience the second time around? I know that it is expensive to attend college, but it is also an investment. It differs from no other investment in that you have to be willing to research the availability of jobs on the other end. You sound like a bright woman - a career test might narrow some other options that have high placement rates, might give you an opportunity to have some income from student loan funding, and might give you some relief from the stress that you are under.
Now, this is just an opinion, but a cat is a cat. I don't think undo guilt is necessary to heap on you right now - list him on Craigslist or find a humane society to help you out.
As for the pink hair - here is my $.02 - take it or leave it - I LOVE to wear shorts and a tank top - no make up - pony tail - hat. But when it come to work - I have professional attire. Do I love that? In some ways, yes, in others no. But I do feel that it is necessary to dress for the job. Unfortunately, to some who have a stereotypical view of the world, individuals who look different scare them. Thoughts they may have are generally negative and unfair.
You have the advantage of choice in this situation. If freedom of expression is that important to you that you would not consider changing your hair color - then be happy with that but know that there are consequences to the choice. One of those might be unemployment. Is that unemployment worth leaving the country and your family? Consider too, whether leaving will be to your advantage or to your disadvantage. I would think, and this is just an assumption, that you would be at an even greater disadvantage to finding work in another country.
I truly hope that you can find a balance in all of this - the thought of not knowing where or what was going to happen in one month is a scary thought.
Good luck in your decision. Take time to think it through.