new cat owner, strange cat behaviour...HELP!!

So here's the story...my friend recently moved to England and didn't want to
take his cat because of the 6 month quarantine laws. He thought it unfair for
the cat. I offered to take her, and he was grateful knowing she would be well
cared for. She has always been a nervous and scared cat, hiding whenever I
would go over, and I don't really know much of her history. The first day she
spent mostly under my bed, and the first few nights were a little sleepless
what with her pretty constant crying and all. She started to come around
through, and grew to accept me, and we became close, of course. Yet, there
are still some strange things she does that I don't quite understand, and
make me concerned.
When she first came I had to change both her food and her litter, as I
couldn't find the same kind of either!!! But I did both gradually, and it
seemed to go fine. I've had her for almost 2 months now. I work fulltime and
am out of the house from 6am until about 5-5:30pm. I keep her fed and watered
and scoop her box regularly and I try and spend as much time with her when I
get home as I can as she seems to need the affection.

About 2 weeks ago I realized she has peed on my spare bed multiple times. So
I washed everything, fine. But just this past Friday, she peed on my bed,
the one she sleeps in with me! I really couldn't understand it. I don't know
when she would have done it either. She's become used to my hours and I was a
little late coming home from work, but the spot was dry when I found it.
Thursday or Friday morning, she also pooped right beside her litter box, on
the floor.
She's also recently become re-afraid of my mom, and even runs from me
sometimes. She has remained VERY vocal, using sounds that make me think she
needs/wants something, meowing throughout the night, and generally in the
morning when I'm getting ready for work. She doesn't seem to want to play as
much as before, although she never really was a big "player". I find that
she eats the majority of her food at night, and if she goes to during the day,
sometimes she stares at it first, or stares and then walks away.

I took her to the vet a week or so ago, but not for these problems. The skin
inside her ears looks to be very dry, and it must bother her because she
scratches them a lot. It gets to the point where little scabs form. The vet
suggested it might be allergies, and so gave me some pills. Well cats and
pills don't go well together, and I've tried EVERYTHING that I could think of,
but I don't want to stress her out too much because she apparently has a
heart murmur.

She doesn't like being picked up, having her ears or back paws touched but
she does love having her gums rubbed and her bum and belly scratched.

I know this is a long, LONG message, but I wanted to put out as much
background information as I could, so I could get the best advise possible.
She has very quickly stolen my heart and I hate to think that I'm doing
something to cause this behaviour or that I'm not doing something to make it
better.

Please give me any help you can.

Thank you in advance,
Sarah