Okay, I'll try be sure to try this. Thank you so much!

That’s nonsense. If OP were actually eating that little, they would be losing weight quickly. IMHO the problem is that OP is not measuring calories accurately. OP, do you have a food scale? It’s very difficult to accurately eyeball calories.

Running is very healthy. Exercise won’t help much in terms of shedding fat but it’s good for your body so no need to stop doing it and feel free to increase as desired. 

The issue with eating so few calories is that it puts your body under extreme stress. It isn’t functioning properly. You won’t be able to push yourself in your workouts the same way. You’ll hold onto water. Cortisol levels will rise.

I am a 5’3” 138lb sedentary female and I eat hundreds more calories than you and still lose 1lb a week. There is genuinely no reason to do this to yourself. Calculate your TDEE, pick either sedentary or lightly active (unless your job is highly active too), and subtract ~500 calories. I bet you could be eating well into 2000 cals a day and still lose.

Should I make any kind of change to my physical activity or do you think what I'm doing should be sufficient?

Yes your calories are too low. Increase to at least 1700 and track diligently, don’t estimate anything, and wait a few weeks to see progress

I've been trying to lose weight for a pretty long time now but I'm finally making progress. I started out as 284 lbs and I'm now down to about 262. That's as far as I've ever gotten but now after about 3-4 weeks I can't seem to lose any more weight than that and the number on the scale had remained pretty consistent. I'm 6"1' and only eating about 1000/1200 calories every day and I know that might seem low to a lot of people but it was never really a struggle for me and I could sustain it quite well especially with the number on the scale as renforcement. I walk 1 mile every five days with intermittent jogging. 

I feel like everything was going right until now and I just don't know what to do. Is my calorie intake too low?  If any of you have any suggestions that would be greatly appreciated!

I made a lot of progress but now I'm stuck, what should I do?