If you have real bulk water issues to deal with there is no such thing as an interior side paint-on solution.
If it's water wicking up from a poorly drained footing it's possible to trench in a perimeter drain on the interior below the slab that could relieve much of it. If the walls were not waterproofed, yet backfilled with a sandy mix much of it could be coming through the walls from the side, no matter how well the backfill drains. (Gravel such as 1/2-3/4" screenings, with a minimum of sand "fines" works a lot better.)
If your roof overhangs are minimal and rainwater isn't ducted well away (as is the case for many concrete & tile roofs) you may get some relief out of a buried perimeter drain comprising of 3-4' of EPDM roofing attached to the foundation about a foot below grade that slopes at least an inch per foot going away from the foundation, with a perforated drain at the outer edge of your EPDM skirting to direct the water elsewhere. See the details on p.6 (.pdf pagination) of
this document.
It's sometimes hard to diagnose the true water pathways even WITH a site visit. I'm not sure if you'll be able to nail it with a web-forum approach. Most moisture problems are bulk-water related, but capillary draw through soils and concrete are quite powerful. Unless the footings are well drained (6" of compacted gravel, no fines) or a capillary break is inserted between the footing & foundation wall it's quite possible that the moisture coming through the wall is being slurped up from the footing.
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