Does she not feel we are a couple?

I have been dating a girl for six months and believe we are in a committed relationship. We haven’t explicitly discussed this, but there is an understanding and neither of us has been seeing anyone else during this time. I recently asked if she wanted to have sex, and she said she avoided it because it caused her physical discomfort. I didn’t respond, but I have been wondering if this is her real reason, or if she still doesn’t feel as if we are genuinely together. I don’t want to broach the topic again because it may upset her or put her off, but I also believe it is important because it will make me feel more secure. I just feel as if I am not sure where this is going, which is why I asked her about it. What should I do?
The simplest thing to do is ask a direct question. If you have given each other six months of your lives, don’t you owe it to each other to have a conversation about what this means, and whether it is going somewhere? Yes, sex is important, but why assume she is lying about avoiding it when you don’t even know what the status of your relationship is? You feel insecure because you have avoided the only question that matters. Talk to her about soon and try to make sure your questions are as clear as possible. Don’t jump to conclusions when you can discuss this like adults instead.

My girlfriend and I have been dating for two months, but neither of us knows where this is headed. She says she wants to figure things out and hopes she will get some clarity as time goes by, but she doesn’t know how much time it will take. Is she just tagging me along for fun?
She has asked for time and hasn’t sent you mixed signals. If you like her and want this to work, why not be patient and give her what she asks for?