Hello and welcome to the Forum.
Looking in detail the picture you have post, it seems that your lamp are fitted with an all-plastic (and awful) European E14 SES (small Edison Screw). If you are living in the US, perhaps you have been in troubles to find and get any bulb that fits in such socket. Don't forget that Ikea is an European brand. Here in Europe we are in the same but opposite situation about lamps of American standards. You problably will need an E14 bulb, but rated at 120 volts (some rare item), or perhaps you shall replace the lampholder for another one in accordance with your standard (E12 "candelabra" or E17 "medium") to can fit regular American miniature or medium lamps into it.
The fact that the manufacturer doesn't advise to use any lamp rated beyond 25 watts, is just due to the fact that those lampholders are so weak that can melt and burn if are fitted with powerful bulbs. However the European "experts" about electric safety, holds that them are
safer than classic ones made from metal (usually brass) and porcelain, so them are approved and almost the only ones availables here. Regrettable!!!
Luckily, are still available in the Spanish market some classic models of E14 and E27 brass-porcelain lampholders made in China that are almost the same that those in use here in Spain until some years ago. Them can be found even in huge quantities although there are not
fully approved for use within the CE
.
Please, let us know more details about your fixture to can help you more accurately.
Regards.