The outside top part of my ankle hurts and is quite swollen. Is that the malleolus which is extremely swollen?

No the tendon is. The bone does not swell. It could be the pl tendonto receive an answer that will be more helpful for you, you need to give more information...Your health status, any problems such as gout, diabetes or blood pressure concerns. You should state how long it has been a problem and what you do to make it feel better. Also tells us what it looks like. Is it discolored, swollen or point tender. The more you t.
Tissue. It is probably the tissue around the bone (malleolus).