Picking up vibrations that set you on edge is not something to ignore--at what point does someone become a stalker? But in the early days of a new friendship, you may have to take a few things into account. Is this someone who is reaching out for help? Someone who is depressed and found a lighted tunnel? Or someone who is out of work or away from work or school on a break and may simply be posting a few more messages than normal?
Play it by ear, but don't dismiss your misgivings, either.