I do want to say that for anyone struggling with an illness who is reading this thread and thinking, "I'll never find anyone," the best thing you can do is to work on putting yourself in a place of being as spiritually, emotionally, and physically improved as you can be--if nothing else, for your own health.
I have also found that some of my depression was probably situational, though I did not want to admit it. From ages 18 through 29, I spent nearly 12 years in 4 pretty much back-to-back long-term relationships. Looking back, I know that I caused much of my own grief because I was terrified of being alone and felt I just had to be with someone. And what do you do when your choices are driven by fear and insecurity? You make a lot of bad choices--at least I did. I chose the wrong people and even worse situations.
I hate admitting this but God has actually been able to bring me to a place of much more completeness WITHOUT a significant other. It doesn't mean I still don't have times when I feel like I'm going to hit rock bottom because I'm alone. I worry about growing old and dying by myself. But I can handle things better now and don't feel stir-crazy stressed 24/7 like I did when I was trying to solve some guy's problems as well as my own.
Do whatever you are able to in order to get healthy--seek counseling, build relationships, find a support network, become established in a church. You may even meet a special someone along the way. If nothing else, you will learn to at least be content in any situation you find yourself in, even if it means being single. I'm not quite there but God has helped me through SO much in the time I've been away from relationships. (I was also prone to being tempted into sin when with someone; not having anyone at least eliminates that temptation, which is a painful but often helpful blessing as far as keeping my life less complicated.)
You may also find it helpful to relocate. I've done this twice in the past few years after living my entire life in one place. It was horribly painful to adjust to at first but you know how when you break a bone, the bone has to be reset in order to heal? The pain I've felt from moving was like a "resetting" of some of my emotional and spiritual skeleton. It hurt like all get out in some ways but when it was "reset" and started to heal, I could finally recognize areas of my life that were clearer and much less painful. I'm still in the process of recovering from this last "re-breaking" but I've learned that the challenge is worth it. All thanks to God, I'm so much better than I was, let's say, even 2 years ago and seem to keep getting better as time goes on. No suicide attempts for probably 13 years and no cutting for around 6 years, which for some of us is a major God-given triumph.
I also like how some posters have reminded us that it's easy to say, "I won't date someone with X" if we ourselves feel we're in a better position. Thank you for reminding me that life can change in an instant and we could go from being the person with all the advantages to the person who now has Situation X in the blink of an eye.
I agree that it's a good idea to keep an open mind because God can surprise us or challenge us with things we'd usually turn down. However, I also believe that part of our growth is learning what we can and can't handle, and being smart enough to walk away from something we know is over our heads. God tells us to love... but also to use wisdom and discernment in doing so.