Sounds like mechanical lower back pain, a central circle of pain about the size of two fists either side of the spine. The pain will be generating from the facets of the spine and will be become sharp from time to time (this will cause the muscles to spasm around the area). This makes the joints closer together which in turn causes more pain
The Sacro iliac joint will almost certainly be dysfunctional but that pain normally does radiate up as high as you mentioned.
you must stop lying on you front (for ever! if possible it is seriously bad for your back) and stop swimming as both of these activities push the small highly sensitive facet joints together- if you must swim only do freestyle (head in water) for the next few weeks. If that still aggravates stop.
You will need to open the joints to get relief. So bend forward and hang. If this causes discomfort you have left this condition for a long time and must now seek passive care. Manipulation and passive stretching will work the quickest but passive stretching + massage will work quite well as well.
The belt is a great idea as it will give the muscles a break/rest but you need to cut out the aggravating factors first.
Have an Epsom salt (magnesium sulphate – muscle relaxant) bath 1kg in bath for 20-30mins then lie on back with knees up and slowly and individually rise the knees to the chest.
my advise go and see either a chiro or osteopath for manipulation other wise find a physio that has done a post grad in the technique. Otherwise go through home management as mentioned above