Finding a comfortable saddle has been a lifelong search for me, however I'm usually fine on just about any one up until about 30 miles or so. 7 miles isn't much to make you hurt so, although you did say you're doing it a couple of times a day on repeated days.
I always ride in bike shorts to avoid chafing, and I think the padded chamois helps too, although not that much - not enough to solve the discomfort you're describing. Did you get your bike fitted by someone who took some time? It's a lot more than just getting the saddle height correct. There's saddle angle, reach to the bars, and more.
I suggest the following:
- get some padded bike shorts. If you don't like the way you look in Lycra, get some baggy mountain bike shorts - they still have the pads.
- Take your bike to the person who sold it to you, describe your discomfort, and ask if he/she will go over the fit with you.
- Bring a multitool on rides with you for awhile. When you notice something starting to be uncomfortable, see if you can guess why. For example: something needs to slide backwards or forwards a tiny bit. Something needs to go up or down a tiny bit. The angle of something needs to be changed a tiny bit (saddle, handlebars, barends, whatever.) Stop, make the tweak, and see how it feels. I've heard Lance Armstrong described as "Mr. Millimeter" because he was so picky about his bike fit - everything had to be within a millimeter or less of what he wanted. It may seem overly picky, and it's a hassle to stop every 5-10 minutes to get off the bike and make an adjustment, but it's so worth it if you can get the fit dialed in just right.
- Keep riding. You get used to it and things will get better. Consider riding every other day or every third day for awhile until you build up your tolerance.
- If the problem continues, eventually you'll probably have to try a Brooks saddle (I like the B17.) I held out for quite awhile, and when I got one I found that it wasn't perfect, but it was better than any of the other 12 saddles I had tried.
I'm no Superman, and I've had my share of sore butt troubles, but I've got things dialed in so that I can ride a century (100 miles) in one day and not suffer too badly. Of course, I don't ride again for 2 or 3 days. I also take tours in the summer where I ride day after day and average around 55 miles per day, with lots of days in the 60's, 70's, and even a few in the 80's (miles, that is.)