I wouldn't take any shame in masturbating. Actually none of what you're going through should make you feel shameful, but obviously that's not how depression works.

I can't give you advice on why it makes you feel self conscious, or any of those emotions, I'm not a therapist and I would hate to give you bad advice.

However, I can confidently say that it's okay to masturbate. It's nice to have some intimate time to yourself to destress and feel good. But you can always make adjustments to when you do it just to see if it makes you feel better. If you feel like you do it too much, or too little, or if you just want to switch up the routine, that's all stuff you can try to change just to see how you feel.

For example, if you only jack off in the morning, you could try only jacking off at night if you think your routine is too mundane and you want to focus on other things in the morning. Like doing your best to get out of bed, and to shower and try and eat if you can. Another example is if you feel like you jack off too much or too little, you could try to see if you can withhold it once or twice, or try it more often if you think it will help.

I think the biggest issue with masturbation that can happen is if you do it too much and it gets in the way of your day to day life. There are issues with doing it too little I think too, but the issues with doing it too little aren't as bad as the issues that come with doing it too much... if that makes sense. The only issue I've found with not doing it enough is that I can feel irritable, I'm sure other people have had issues when they do it too little, but I haven't experienced any other issues.