Kinda was in a similar spot a few years ago, but I was staying at my mom's, she adopted two rescue kittens (in addition to the two cats we already had), but she was gone a lot more and I was there at the time a lot too, and one of them was kind of a douchey, needy, a-hole and would cry if he went without some kind of attention for 45 minutes until he got what he wanted--which might be to play for 4 hours straight or have a third can of food of the day by 5am or something that at the time I shouldn't have or couldn't have done. The noise drove me batty, the idea that half of my actions were to serve a cat I objected to in the first place drove me batty, his brother that was very physically affectionate too drove me batty, the holiday season drove me batty. I ended up involuntarily hospitalized because my eating disorder got really bad (but the place I went to stated they don't do anything with eating disorders, so I essentially was locked up for 10 days just to be driven further to insanity by nurse's not understanding crap and being switched rooms or at least roommates every other day (up to three times in a day, really). That was the IP stay I went in NOT psychotic and came out having absolutely zero sense of reality.

Alright, getting off track, but do talk to your therapist about it, ask yourself if right now is the best time to be solely responsible for another life (I'd say if you're generally doing as well or better than usual you'd be good, but if it's a rougher patch of life that's been sustained for reasons other than the pup then maybe think about alternatives--maybe you know someone who can help you out more or can take care of him as needed? As much as I hate to suggest this, but even giving him up if you can't take care of him or arrange someone who can when you really need a break would be better for both of you than keeping a dog that won't get the full Fido experience of having someone who can (and does) provide that.

There's also this DBT skill called "cope ahead" which is basically catastrophizing but instead of worrying about the worst-case scenario, you plan for it so you can handle everything on the spectrum of scenarios. I think looking into that might be of some use here.