I have a feeling that the girl I am dating is not as into me as she claims to be. She says she loves me and wants to have a long-term relationship with me, but I also sense a certain lack of commitment when I ask her to do something that inconveniences her in any way. It’s not the kind of behaviour I would expect from anyone who claims to be in love. For example, if I ask her to accompany me to a family event because I don’t want to go alone, she will make excuses and say she has other things to do even though I know she doesn’t. She laughs it off when I bring this up, but I just don’t get that feeling of security from her. Am I being strung along until she meets someone better?
If you aren’t feeling secure and your feelings aren’t being taken seriously, your relationship is not going to work out. Actions always speak a lot louder than words, despite how clichéd that sounds, and you shouldn’t be gaslit into thinking that everything is fine if you don’t really believe it. Try calling this out a few times and don’t shy away from being honest about what you think and why. If it doesn’t lead to any positive change, or even real dialogue, you should assume that this won’t last for much longer.

Is it normal to be scared of having sex with someone after dating for just two months? I don’t know if I am being prudish.
There’s nothing prudish about knowing your body and choosing what you want to do with it. If you aren’t comfortable with something, say it and stick to it because no aspect of a respectful relationship should be forced. Draw your boundaries and ask your partner to respect them because that is how you will both grow together and build a strong bond. Do what you want to only when you’re ready, because that’s the smart and healthy thing to do.