Often that is a symptom of having a little tube caught between the bead of the tire and the wheel itself. In fact the exact symptoms you describe are very common with this problem.
The way to check for this is to inflate the tire part way and look at the edge of the tire next to the rim all the way around on both sides. If there is one section that is not as well seated as the rest, it might be the tube pinched in between the tire bead and the rim. If there is a place where this occurs deflate the tire and see it any tube is pinched in there. Before each inflation with only a very little air in the tube go all the way around each side of the rim and push the tire in gently to see if there is any tube pinched between the tire bead and the rim.
Also if you are installing with tire levers be very careful. Most tires can be installed without them, roll the bead over the edge of the rim with both thumbs at the tight spot don't just push it.
I also inflate the tube just a little to get it up in the tire away from the bead. If you are new at changing tires ask a shop to show you what I mean about rolling the bead over the rim.