Hello, I am new to road cycling, I been riding for a year now and starting to loose weight. I am getting in shape and I look thinner now, I lost like 13 pounds. But I also noted that I am like loosing width in my back and chest. All my formal shirts fit big now, the same for sport coats. It like I have to put most of my wardrobe in the trash.

Is this normal?

Yes, if you lose weight it is normal for your clothes to seem large.

If you were to gain weight, it would be normal for those same clothes to seem too small.

Yes it's normal to loose a lot of upper body muscle when doing only cycling... That why it's good to cross train and include strength training and weightlifting...

would only weightlifting be Ok?

Weightlifting is strength training so you'll be ok.

Suspect it's just fat you're losing not muscle mass. Simpler to just buy some new clothes unless you intend to add and maintain substantial muscle mass for the rest of your life.

Yes, I guess, I thought I would only loose volumen in the stomach, not in the chest, back etc.

I think you will find that fat generally is lost from the fat cells all around your body. People who have lost a lot of weight even have to consider getting new shoes because the old ones they were when heavier become too sloppy in fit to wear comfortably.