Thanks for the additional information. Often a dog will start eliminating inside if it is uncomfortable going up or down steps or outside for some reason. A disc issue can make going up and down stairs painful or potentially painful which can cause a dog to not want to go out. Since he has known allergy issues, he may have difficulty breathing outside and thus is avoiding going out. If he is on medication to correct the allergy condition, it may take getting him outside a few time (when the medication is working) so he sees that it isn't an issue any more.
An alternative would be to put up a patch inside for him to eliminate on. You take a large pan like a kitty litter pan or even a baby swimming pool. You create a platform frame with wire on top. Place newspaper or other absorbent material such as wood shavings under the platform and place sod on top of the wire frame. Normally I suggest sod and paper but he is allergic to grass and wood, etc. So you might need to use a pvc frame, kitty litter and finer screening so dirt can be used over the screening to give the feel of outside without creating an allergic reaction. You can remove solids and can spray the urine so it moves through and down into the absorbent material underneath. This lets you use the same dirt for a while before needing to replace it. You do need to replace the material under the platform.
You might try a dap collar wihich uses pheromones to relieve anxiety and that might help some. They are available online and pet stores. Your vet might prescribe medications for anxiety such as xanax as well that might reduce his anxiety and get him back outside.
I strongly suggest obedience training daily so he doesn't hesitate to obey you even if it is something he doesn't want to do like go down stairs. Training should be ongoing. The following site is helpful in helping owners train their dog. Be sure and click on the link to the page on obedience at the bottom. and links on subsequent pages leading to detailed instructions.
Training works best if you train at least 30 minutes a day (two 15 minute sessions). I would start making your dog work via the Nothing in life is free program (NILF). It is outlined below.
He might also feel he can't protect himself if he is muzzled all the time outside. This would also cause him to not want to go out. You might look at the BAT method of correcting aggressive behavior
so that he doesn't have to be muzzled. I do hope you are using a basket muzzle since other types of muzzles can interfere with breathing and with his allergies, that might be dangerous to him if he had an inflammatory reaction. Here is the site on BAT.
I hope this information is helpful to you. If you need more information or clarification, please reply and I'll get back to you as soon as possible. If you are satisfied, please take the opportunity to rate.