I highly recommend getting a better tool (or tools). While conceptually there is no difference between a power screwdriver (which you have) and a real drill, the drill will (if it is any good):
- Have adjustable speeds. This lets you go slow to get started, speed up to get through a lot of material quickly, slow down when you get to tough parts, etc.
- Have a much higher top speed. That really makes a big difference. A power drill with a single high speed (which I wouldn't recommend, but hypothetically) would be much more effective than a typical power screwdriver at drilling through most substances.
- Produce a lot more torque. Meaning on the slow-but-tough parts you'll have a better chance of getting through than with a power screwdriver.
You don't have to spend a lot, though of course budgets vary and many (myself included) don't want to spend much for a one-off. My recommendation is to pick a brand/type of rechargeable tools that you are comfortable with (ideally sold in local store, lots of other tools available that use the same batteries) and get a starter kit - tool + battery + charger. Most brands now have an 18V or 20V group and that's what I'd recommend. You may do OK if you can find a 12V batch at a really good price - but they may not have the power to handle the tough stuff.
There is one more key issue: Regular drill vs. Hammer drill. A typical regular drill just turns a bit - fast, variable speed, forward/reverse. A hammer drill (essentially) bangs that bit back and forth while turning it. Most hammer drills can also function as a regular drill. If you are working exclusively with wood, plastic and metal then a regular drill is all you need. But once you get into brick/block, concrete and similar items, a hammer drill makes a huge difference in productivity. Trust me - I found out the hard way and added a hammer drill to my collection (using same battery I already had for a regular drill). Ceramic tile is a bit of an in-between - with a bit of help getting started (as explained in other answers) a regular drill on high speed with a good sharp bit should do just fine. Actually, for a simple clean small hole in typical ceramic tile, you probably don't want to use hammer mode as it will make the hole (great!) but pretty quickly expand to "crack the rest of the tile to bits" (usually not so great). But a hammer drill with a half-way decent regular drill mode and a half-way decent hammer drill mode would do well as a starter rechargeable tool for general DIY use.
I would consider something like this starter pack from Home Depot:
Charger, 2 batteries, hammer drill. Not the fanciest/"best", but good enough for typical DIY usage, compatible with plenty of other tools if you want to add more later on, and a lot more powerful than any power screwdriver that I know of.
(I have no connection with Home Depot or Ryobi, just a satisfied customer. You may do better with something else depending on your location.)