You ask:
How to avoid radical skepticism?
Throw a rock at a philosopher and steal their strategy? Everyone from Pyrrho to Robert Audi has a solution. You can start by not reinventing the wheel, one of the advantages of attentive study. Consider any one of the strategies following from the WP article "Philosophical Skepticism". But you have to find something that appeals to your intuitions.
However, if you're looking for something sophisticated and contemporary, consider the arguments put forth for process reliabilism (IEP) which essentially puts forth the following claim:
Process reliabilism, by contrast, asks whether the general belief-forming process by which S formed the belief that p would produce a high ratio of true beliefs to false beliefs.
In other worlds, it's simply an undeniable empirical observation that if one subscribes that truth exists, it's simply probabilistic that given billions or more epistemic agents, most of them will find a way to justify their beliefs and produce knowledge.
You say:
Whenever I try to solve a problem philosophically, I always end up at radical skepticism, where the solution is unprovable. I understand that skepticism leads nowhere, but I always tend to seek absolute certainty.
Lastly, you can abandon the need for absolute certainty by rejecting such a thing exists as is done in embracing fallibilism (IEP). What's wrong, after all, of accepting there is uncertainty in life, as long as its a reasonable amount in some context? From the article:
Fallibilism is the epistemological thesis that no belief (theory, view, thesis, and so on) can ever be rationally supported or justified in a conclusive way. Always, there remains a possible doubt as to the truth of the belief. Fallibilism applies that assessment even to science’s best-entrenched claims and to people’s best-loved commonsense views. Some epistemologists have taken fallibilism to imply skepticism, according to which none of those claims or views are ever well justified or knowledge.
To me, the best way of doing that is embracing some of the principles of van Fraassen's constructive empiricism (SEP) and replacing the notions of correctness with adequacy. Instead of asking, is it certain that I'm correct, you can ask, is the conclusion I arrive at adequate to describe the world to accomplish the goal? This of course moves one's epistemology, even natural, towards pragmatism (IEP). From the article:
Pragmatism is a philosophical movement that includes those who claim that an ideology or proposition is true if it works satisfactorily, that the meaning of a proposition is to be found in the practical consequences of accepting it, and that unpractical ideas are to be rejected.
And if all else fails, and you are stuggling intellectually and emotionally, consider whether you are on the obsessive-compulsive spectrum with something like OCD or OCPD. Some problems are not epistemological or logical, but psychological, and there's no shame if you are neurodiverse. If a fixation on certainty leads to paralysis by analysis, it may simply be a matter of taking an SSRI to change how you think. Perfectionism, properly regulated, is an inspiration for quality, but if becomes pathological, there's no more shame in regulating than there is in diabetes.