Did you prime the shelves before you painted? There could be several reasons why your paint isn't drying. If the previous surface wasn't sanded and primed, your paint may not have had anything to adhere to. You said the boards are enamel. That tells me the boards are not able to receive the oil paint. The oil paint will dry but another one of your problems is the fact that there isn't much if any ventilation in the closet so the drying process is much slower than it would be in a well ventilated area. You can certainly remove the paint and start over which is what I would do. If you decide to start over, sand off the enamel, prime then paint. You will be happier with the results.
Note: There is a drying additive you can mix in your paint but this must be done BEFORE you paint. Check with your local paint store, Lowe's or Home Depot.
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