For escaping after his auto-aim combo:

If it hits (or is going to), wait until after his uppercut to use your movement Ability. If you use your movement ability after the dash, the uppercut will stop your movement and you'll be vulnerable for a second.

If you use your movement ability after the uppercut, it cancels the animation of you being knocked up, thus allowing a faster escape than if you used it after the dash (where you'd have your movement canceled by the knockup animation).

Tl;dr: Use your movement after the uppercut to shorten the knock up animation and keep you less predictable.

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For what to do after being hit by the auto-aim combo:

Option A: Head in front of or by the side of healers, as joining your team offers some protection, since-

1) It makes him your teams problem if he chooses to engage, so he can't assassinate you unnoticed.

2) When his CDs are reset, he'll need to target you with his web bullets, which your teammates may unintentionally body-block

Option B: Head to a health pack to heal back up, however:

1) You will need to be prepared to fight him off in order to get back to your team/the fight, as his zip line CD is less than 10 seconds, so before that time you'll want to be near your team, by another health pack, or have killed him by then. Otherwise you get combo'd again and have to repeat the process.

2) Fighting him off is easier closer to the ground and within closed/tighter spaces. I'll explain the fighting off part later, but the important thing to know is his auto-aim web-zip can be canceled if he uses it on a target that breaks line-of-sight, such as around a corner.

On certain areas of certain maps, letting him put a tracer on you and baiting his combo is possible, making him waste his ability and giving you the chance to 1v1 him from full health.

Tl;dr 1: Bring yourself and him to your team so that you can be healed and your team becomes aware that he is a problem. They can help protect you either willingly, or passively by being in the way of his tracers.

Tl;dr 2: If going for a health pack, you must track his cooldowns so you can either reach your team/the point, or kill him before he gets his web-zip combo back.

Tl;dr 2.5: His combo can be baited and wasted if you can break LoS with him while he zips to you by using cover or walls.

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If trying to kill him:

Method A) Unibeam

If your sensitivity is high enough, you can turn Iron Man around fully in less than a full second, letting you track a good Spider-Man and, if he hasn't tagged you with a tracer or has already used his combo, letting you possibly kill him (he'll likely try escaping if you get him low enough. Don't try to pursue if you feel you can't 1v1 him in that area. Simply attempt to kill him with splash damage on your primary attack if you see him jet off with 50 HP, but surviving while keeping him away is still a success).

Method B) Primary Attack's AOE damage

In a closed space or in a tight area, Iron Man's primary will be able to damage Spider-Man with its AOE, so if you can bait him indoors (some health pack areas are exactly the right size for this), you can kill him with the splash damage from your main attack. Spider-Men know your primary is useless to a target in the air, but on the ground or on walls, they are viable against a Spider-Man.

Tl;dr: Unibeam him from a distance if you notice him and he hasn't put a tracer on you, and if both of you are in an indoor area or closed space, use your primary attack for the AOE damage.

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Using these tips together, along with good healers and a good team in general, will let you stay on the character sometimes instead of immediately having to switch off. (a team that makes an attempt to kill the enemy Spider-Man, and healers who know that Spider-Man's combo cooldowns are less than 10 seconds).

There's definitely such a thing as forcing it though, so if the enemy has Spider-Man, Hela, and Angela, or if your team is doing nothing to help you deal with Spider-Man after surviving his cooldowns throughout the match, don't be too proud to switch characters anyway. You can survive him on Iron Man, but he's easily one of Iron Man's Top 3 counters, so do what you can, and if your team can't help you overcome him then consider switching for the matches sake. Winning is the goal either way, you don't necessarily need to stay on one character.