We've always draped our towels over the same rod as the shower curtain. It is only a tension rod and have never had any trouble with 'pulling down'. It normally has two towels on it and our shower curtain is the kind with the liner on the inside and decorative fabric piece on the outside. The weight has never been an issue. A double rod would certainly look nicer than what we do now, but looks were never what we were going for.

The height of a shower rod relative to the position of a tub is largely a matter of use and desired effect. Some shower curtains extend almost entirely to the floor while others drop just below the rim of an attractive claw foot tub. What is certain is the shower curtain liner needs to hang down into the tub below its rim so water does not splash onto the floor. Hanging a Shower Rod Shower curtains are commonly 6 feet in length from top to bottom. They are made longer as well. For custom bathtub designs, their length can vary greatly. If you are installing the shower rod anew and need to know where to hang it, the first thing to do is measure the length of the liner. If it is 6 feet long, figure that it should hang below the rim of the tub at least 5 inches. That means the rod should be placed 5 feet 7 inches from the top of the tub. However, consider the difference between the rod placement and where the liner attaches to the curtain rings. If the liner dangles 2 inches below the rod, you can add that to the height of the rod, placing it 5 feet 9 inches above the tub. The curtain also requires some consideration. It should not drag along the floor; rather, it should be at least 2 inches above it when hanging. If you want to showcase a claw foot tub, hang the curtain just a few inches below the rim of the tub. Here is a link that might be useful: shower rods

Carolyn - I can see a couple of reasons people are reluctant to drill holes into tile: 1. If a cheap rod is used it might get dented or rust and screws of replacement rods might not match the existing screw holes. 2. If the holes are situated below the shower head, you will risk that water will seep behind the tiles, leading to mold and all its accompanying messy and expensive issues. This potential problem can be avoided entirely by filling the drill holes with epoxy and insert the screws through the fresh epoxy. 3. Some people just don't want any holes in their expensive, beautiful tile. That said, we opted for screwing our rounded aviation-grade aluminum rod into the tile of our kids/guest bathroom. We will never need to replace it and we don't have to worry of a flimsy tension rod collapsing onto our kids or - gasp, guests taking a shower. Here a pic of our kids bathroom:

You'll be fine with a curved rod. I have a curved single rod in a similar tight setup next to the toilet (however, mine is not a tension rod). I usually leave the shower curtain pushed open to the right (non-toilet) side when not in use to make the bathroom appear larger. I tried several different shower hook options. These were the winner by far (especially for ease of taking curtain on/off which was important in my case because I have an extra tall shower curtain I have to get on a step stool or small step ladder to reach the top of): https://www.amazon.com/gp/product/B017DM37Z2/