Egoists can certainly go into melee
After all, modifying yourself is what psychometabolism is all about. Metamorphosis of various levels, empathic transfer, hustle, psychofeedback, fission, and fusion are pretty good discipline powers for this. Off the main list, vigor is phenomenal, share pain is definitely not bad (and even great if you share it with a psicrystal), and temporal acceleration is excellent. Also, definitely do not be afraid to deviate sometimes from your desire to melee: a major part of your advantage over other melee warriors is you will have answers to problems that “hit it with a sword” can’t solve. Teleports and flight, area and ranged attacks, things that obscure vision, and so on, can be very useful.
Transmogrifists seem better than Egoists
Transmogrifists are a slightly different form of Psion Psychometabolism-specialist, but the ability it gains at 8th level is more appropriate than what an Egoist gains. The 20th level ability, I don’t like very much, but that’s only at 20th level.
Everything else about a Transmogrifist seems pretty much identical to an Egoist.
Phrenic Slayer is a very good choice
The Phrenic Slayer prestige class gains full BAB, and a number of rather potent defenses, including the excellent Cerebral Immunity. Highly recommended.
Do consider other psionic classes
Both Psychic Warriors and War Minds (who use the Psychic Warrior list) gain quite a lot of Psychometabolism powers, including powers that Egoists either get later or not at all. While Egoists can do well in melee, and in fact the potency of the Psion list can actually make them better at it, these classes are designed for it, which makes it easier.
Psychic Warrior or Psychic Warrior/Phrenic Slayer is better for straight psionics than War Mind, but War Mind is only 10 levels long which allows you to also do other things if you like.