Okay, so first of all, if the two of you aren't in physical proximity, the odds of having any kind of real relationship are vanishingly small. So I would recommend writing off this whole "relationship" from the get-go.
Second, while compliments and comments in the moment may feel nice, the emotional rollercoaster doesn't feel nice. It is good that you recognize this. Now you need to get off the rollercoaster.
Third, a lot of people are talking about what her intentions might be. My policy is to be honest and to generally assume honesty. She says she is complimenting you to help boost your self esteem. This is very nice of her, and you should appreciate her kindness, even if it is misguided.
Forth, the important part - action. Tell her that you appreciate that she is trying to boost your mood, but that you've found that the emotional rollercoaster it puts you on makes you feel worse overall. Ask her to stop. If she doesn't stop, tell her firmly "I've asked you to stop doing this. Please stop now or I will stop talking to you." If she continues, stop talking to her. If this is a problem within your group of friends, reach out to friends individually and explain the situation from your perspective, and ask for their understanding as you maintain your personal boundaries.
This should solve your immediate problem. However, you have a bigger problem. Why are you even hung up on this girl at all? She doesn't live near you. You don't seem to know what she looks like. She is violating your boundaries and making you feel bad. Why do you give a single flying fuck about her? Well, the answer is obvious to everyone here - she is the only woman in your life who has shown you any kind of romantic interest lately. You have no options, so even a bad option is enough for you to get all emotionally tangled up. And the solution to this problem is equally obvious: go find more options. It's like you're asking us if it's safe to eat the moldy bread in your cabinet because you forgot grocery stores exist. There are 4 billion other women on the planet - go talk to one who isn't on the internet!