Uncertainty

I have been Hsv1 positive and have known because I’ve had cold sores before. I am sexually active and have given and received oral. I recently developed psoriasis and went to a dermatologist who diagnosed me. I have it on my elbows, scalp, and belly button. At the same time I developed red spots on my penis. They are non painful last for months at a time with application of cortison creams. They are scaling, dry, red, and skin peels around the area. I am going in for a follow up next week and going to bring it up to my dermatologist which is a little unnerving. I am just thinking about it a lot lately and just wanted some clarification. Can hsv1 on the genitals be non painful non ulcers? I have used valtrex for my cold sores but they don’t seem to do anything as far as my redness on my penis. The only thing that has helped has been psoriasis creams. Anyways. Just be happy to hear some thoughts. Thanks.