How large are the bites? I have never had a spider bite (knock on wood), but I hear that they are usually a little more tender rather than itchy, and often do look a little more like a sore rather than a red bump. I get bitten by mosquitoes quite often and do find that ant bites can be a little more tender for me. Also, I used to have a mild ant allergy that I grew out of it. The bites would swell up to about 2 inches in diameter and would harden. Luckily this hasn't been happening anymore.
If the bites are very small and are three in a row very close to one another, these are often caused by bed bugs. They nickname these kinds of bites "breakfast, lunch, and dinner." The bug will move on and bite the next spot, and the next, when they get interrupted (for example, you move in your sleep). Hopefully these aren't the case! I have had these similar bites before but could never find any signs of bed bugs. Now I have a new mattress and this time around bought a special cover to help with allergies, so I better not have any bed bugs!