Well, first off, I am sorry that you are going through something that is obviously very upsetting and has you on edge no matter what it is. Just the fact that thinking someone else could sense you were unhappy made you so upset seems to me to be a sign that you need to really talk to SOMEBODY.
It sounds to me like this other mom meant to be kind. Maybe she has been through problems in her past that few people knew about and she just sensed the same feeling in you. In the end, it does not really matter if she just realized it through intuition or observation- she saw that you were in pain and tried to reach out to you in a helpful way, so I would just take that for what it was : a kind gesture from someone who was concerned about your well-being.
As for whatever problem you're dealing with- don't face it alone, no matter what it is!
When my marriage began to have problems, we went to counseling that always seemed to end up being all about my husband and never made any difference because he would not follow through. I got sadder and more and more worried and almost no one knew about it. I was too ashamed to tell my family (who lived in another state) and my husband acted 'extra' happy and attentive to me in public and in front of friends. I felt like no one would even believe me if I tried to tell them what was going on- totally isolated.
But when I finally broke down in front of my girlfriends- they had all suspected something was wrong and just hadn't been sure if they should say anything! They were SO supportive and practical and helpful and made it clear that they were there for me, no matter what ended up happening.
Same with my family- deciding to leave my husband was the most difficult thing I ever did. My parents were horribly upset when I first told them I wanted to get a divorce- but my ex's lack of doing anything to stop it eventually convinced them it was for the best and they too were super supportive.
What I am trying to say here is that people will want to help you and give you some guidance that you need, if you let them. I am not saying you need to confide your personal business to this other mom whom you no longer know really well. But- I would start by seeing a counselor or speaking to your minister or someone you feel comfortable talking to about whatever is going on. Bottling it up inside of you and trying to cope with everything yourself will not last forever and is soul-crushing- I know, I was there!!
It sounds like this other mom really just wanted to help. Let her- or someone else- be supportive of you! You will be amazed at how much it can help, just knowing you are not in the situation all alone.
Best of luck to you- get some peace of mind if you can!