My situation was a little different, but I could relate.
My husband and I married before he joined the military. I wasn't happy about it and after seeing him for a few days for graduation and flying back home I told him I think I want a divorce. He was crushed and going through ATT at the time.
We still talked for a month after with me waffling between (it really wasn't fair to him), but I was anxious and depressed and the distance just made it all worse. Soon after when I was out of country for a month, he told me he's done and wants to give up. It fucking hurt and I deserved it. I cried and I still remember pacing around saying "no, no, no, no" which didn't make sense, considering I was the one that originally told him I wanted a divorce.
Either way, it really put my ass in gear and made me realize that I was frustrated and upset about him joining the military and that I was taking it out on him. I was also just really depressed. I didn't like the "lifestyle" as a kid (my dad did 20 years) and knew I wouldn't like it as an adult.
It took us a year or so to fully work out most of our problems. The first few months after that was really hard. It made me realize that I was such a complete asshole to him and I didn't consider his feelings and wants much at all. I've improved immensely as a person and sometimes my husband will get teary-eyed and ask why I've changed (for the better). I feel guilty when he asks, because I know I was a terrible spouse. I wish I had been a better partner years earlier.
It's been a few years and we're in a much better place. The complete breakdown our relationship suffered helped in some ways. It did improve our communication by quite a bit.
As for you, if your boyfriend is ignoring you then he might've completely given up. I don't like telling people how they feel, but I'm going to right now and say you should feel awful for giving him an ultimatum. It's not a nice thing to do, especially when you need to work on yourself. Your SO isn't supposed to be your only support system and not only that, but you should support him in his wants/desires.
I won't tell you if you should just permanently break up or work it out. I do think you need to work on yourself if you can't understand where your SO is coming from, which it sounds like you don't. You're not really taking responsibility in any way and you're right that it does sound really selfish that you're "going through a really rough time." You're taking it all out on him.
If he's up for it and you're serious about committing then work on yourself. No ultimatums or saying anything out of anger, because that hurts your relationship more than good. Step away, take a breather, but be sure to communicate why you need a moment to yourself. Be nice and considerate. I'm not saying don't tell your SO your anxieties or about your depression, but don't 100% rely on him to help you. My husband will try to comfort me by giving me a hug and saying "I'm sorry, is there anything I could do?" because that's about all that could be done. We usually leave it at that unless it's worse than normal (same for my SO as he also has depression).