To identify the best sites for you, it would be helpful to know what makes you uncomfortable. For some, it’s the current, which you mentioned in your original post. For others, it is depth. You also mentioned being at 60 feet. For others, it might be swim-throughs, or being out on the wall, where there is no bottom in sight. I haven’t taught in a number of years, but my experience as an instructor tells me that the best sites for new divers are relatively shallow, with little current, a hard bottom, and no swim-throughs. It’s actually not easy to find sites that meet all of those criteria in Cozumel, where the sites tend to be at least a little deeper and there is generally current. I think one of the best for newer divers would be Chankanaab. It’s maybe 30-40 feet, hard bottom, and the current is generally mild. Maybe the best for new divers would be Columbia Shallows, 30 feet or less, hard bottom, and no current or mild current. But It’s very far south and dive operations are often reluctant to go there. It takes a lot of time, making it hard to stay on schedule for afternoon dives and it burns a lot of gas. I’ve seen lots of snorkelers there, which is an indication of its appeal for those who aren’t ready for deep dives on the wall in heavy current. Yucab is usually good for new divers, but sometimes the current gets stirred up. I have seen downcurrents and what amounted to a whirlpool there. It’s rare, but you never know. Dalila and Francesca have hard bottoms and the current is usually mild, but they are more like 50 feet or so. Two of my favorite dives - lots of critters. There are actually several Palancar sites. Palancar Gardens is good for new divers, relatively shallow and the current is usually mild. You can get out on the wall, but you don’t have to. Palancar Caves is mostly swim-through and out on the wall, so not good for new divers. Most of Palancar Bricks would work, as long as you don’t get out over the wall. Paradise is a good reef for new divers, relatively shallow with a hard bottom, but there can be some current.
I would suggest trying Aldora Divers. They are really known for catering to advanced divers, but they have seven boats, so they can group divers by experience levels. This can make it easier to get to the sites you should find comfortable. They have some dive guides who are particularly good with new divers. I’ve been on Aldora boats with newer divers when I wanted to do an afternoon or night dive and there was only one boat going out. I have been impressed with how well they work with new divers. Their rates are higher than most other shops, but I think you get good value for the money.
Good luck, breathe slowly and deeply, and enjoy!