Is it normal i gained weight without eating more?

I have hypothyroidism, just got diagnosed a yr ago. I gained like 30 pounds in a yr. People are telling me there's no such thing as gaining weight from eating the same amount, that I must be eating like a whale to get from 125 at 5'4 to 155.

The people who say this are two people at my work. They tell me I need to stop eating because I used to be so skinny and now I'm fat (they're not fat-they're like 98 pounds at 5'5 and 115 maybe at 5'3). I tell them I eat the same and that I think it's from hypothyroidism because according to my Dr, the rate at which I burn calories was 10x lower than the average person for so long that my body started gaining easily/storing fat immediately. They just told me I'm a liar, that I must sneak food because no one can gain weight from a health condition. They told me I'm ridiculous and stupid.

This makes me feel really down about myself. I figured maybe I am eating more than I should. I joined a few calorie counting weight loss websites because of this as it seems like good motivation.

According to these websites, if I want to lose weight, I have to cut 500 calories a day to lose 1 pound a week. I spent two weeks making sure I calculated my average daily caloric intake. That is 1010 calories a day. That means I'd have to eat 510 calories each day to lose weight (cut 500) so that's what I'm gonna do but I feel that is hard. I eat an egg for breakfast, I only drink water for my beverages, I eat a banana or apple for my snack, my lunch is usually tunafish on a slice of tomato and my dinner is usually a salad with mixed veggies (I'm a vegetarian).

I don't know what to cut from my diet. I already exercise at the gym four days a week for 2 hours and I take my yoga class on saturdays for 2 hours. is it normal to gain weight for no reason or am I doing something wrong? My goal is 90 pounds because people call me obese right now at 155 even tho I'm only overweight by 9 pounds.