If she is physically healthy she will eat when she's hungry, especially if you can be calm and patient.
My granddaughter didn't like the bottle when my daughter stopped nursing her. We tried different nipples and bottles until we found one that she liked. Until then her mother or I would hold her and put the nipple in. She'd swallow a little bit and push it out. We waited a few minutes and tried again. Swallowed some and pushed it out. When we got tired of it we quit even tho she hadn't drank enough. And repeated the routine later.
It was important to feed her at the first sign of hunger before she was overly hungry. I don't remember how long it was before she was nursing on a bottle with no difficulty.
Looking back I wonder if it was the formula that she objected to because she had taken bottles, with breast milk, in between nursing on the breast. Eventually the dr prescribed a dairy free formula after testing her for allergies. She drank that fine.
During this difficulty with the bottle she continued to gain weight. The only time you need to be concerned about eating is if she loses weight or doesn't gain over a period of time.
As to solid food perhaps she's not ready to have solid food yet. For her to eat solids her digestive system including her ability to swallow solids has to be developed.
Six months is early in the window of when to start solids. My granddaughter's pediatrician suggested that it was better to start later because the baby is less likely to develop allergies when food is started later.
If your daughter truly isn't eating, is lethargic, or appears ill you definitly should take her to the pediatrician.
If she's not ill, she really will eat when she's hungry if you are able to be calm and relaxed about it. If you're anxious and tense she will pick up on that and may not be able to eat. It's important for meal time to be pleasant for both babies and adults. When you say she cries when the spoon reaches her mouth I suggest that perhaps she associates that spoon with pain, either physical or emotional.
I just picked up on your description of your daughter being "stubborn and knows exactly what she wants and likes." That's good. A passive baby may be easier to care for but they have their own set of problems as they get older. Both of my grandchildren could be said to be stubborn but that has such a negative connotation to me. We call them strong willed. It is frequently good to give them what they want at 6 months, especially food. The parent should make reasonable adaptions to their needs. If we fight with them over everything we are reinforcing their stubborness. I don't know if stubborn has a negative meaning for you. If it doesn't please disregard this paragraph.
To reassure you, no healthy baby ever starved if food was available to them. They will eventually eat.