<human>: Can you condense the text into a few key points?

I have been going out with this woman for about a month now and we are in the 5-10 date area. She has met my friends and I have met some of hers. We go out on dates/do activities every week but I am uncertain about what to do now. We both don't have a lot of relationship experiences because of our various backgrounds that I won't get into here. I know I am in particular very shy / reserved in public when it comes to PDA and relationships. We haven't done anything more than kiss each other on the lips and hug. What is generally the next thing I should be trying to do? We're actually connecting pretty well on the emotional level as we've both discussed our backgrounds, families, siblings, childhoods, etc. I just feel we are not making as much progress on the physical level (whcih I do believe is important as well).

I don't want to come off as creepy but I don't want to be seen as asexual either. As cheesy as it is, is time to start holding her hand every time I see her and putting my arm around her when we watch movies and other such things? Should I just come out and bluntly ask her about this? (Could she be asexual?)
<bot>: We're both inexperienced in relationships and are now entering the 1+ month / 5+ dates range, what should I do now to increase intimacy (not necessarily sex)?