You don’t have to go to the gym to increase fitness, it doesn’t hurt, but it’s not required, especially if your fitness level is low.
I’d suggest taking the advice already given and “don’t sweat exercise” at this time. You might find you still lose weight AND feel good. Eventually, you may feel more a desire to exercise, when/if you do, I’d suggest walking, on a treadmill, outside, at the mall, where-ever, just go for a walk for time, say 10 minutes at first, then increase. If using a treadmill, you can play with increasing the incline while keeping the speed low, this is low impact and low stress.
Now, until you are ready to “step it up” here’s what I suggest, be in-efficient in your daily activities. Here’s what I mean by that: when cleaning the house/putting things away, take more trips through the house then you have to. If you have two things in the dining room that need to be taken to the shed, take them one trip at a time. If you are parking at the grocery store, park out as far as you can and walk down isles that you don’t need anything in (unless it’s an aisle that will trigger a non-keto purchase), when folding the clothes, fold one item, walk it to the closet/dresser and put it away, repeat. Walk to the grocery store/library/work if you can (win-win, you save money AND get movement).
Adding these simple “in-inefficiencies” to your day will result in more motion on a regular basis, maybe precluding the need to even head to the gym.
Good luck to you!