As Sebazy said, a lot of how exactly the exchange went was unfortunately on you.
Stating that you're old school doesn't help because it sounds simply like a silly excuse that people that want to semi-afk/ pretend they're pure healers use. While I don't agree in how the others adressed it, their point is still valid: a healer should dps.
There is not enough incoming damage in this game to justify a healer only healing and deliberately using weak skills so they look busy with healing, which some of the pure healer types like do to, doesn't make it better either.

You have several options:
1) set priorities for your keybinds and unbind some skills that are less important to make room for the 3 dps buttons. From what you said you have access to about 20 buttons. 3 dps skills makes it 17 - that is plenty for healing skills. Things like Emergency Tactics, Summon Fairy, Physick or Protraction can be clicked if needed but chances are you'll be entirely fine without these skills after summoning your fairy at the start of the duty.
2) get hardware that is better suited for you. You can try a controller or a MMO mouse, the latter starts as low as 30€ but even in other countries you'll not have to pay a fortunate to get one if you order online
3) tell them about your injury - most people will immediately be understanding but if you get a competent tank he won't need your healing and may tell you so you'll be back at square 1. Also keep in mind that dpsing is only an additional 3 buttons just do to the basics in both aoe and single target so it can still come off as an excuse to other players.

The last option is the worst in my opinion because with all due respect to injuries (and I don't know exactly how bad it is for you), there are plenty of ways to work around them that you could at least try in order to make room for 3 buttons so not dpsing at all while there are other options would mean you'd deliberately not contribute when you could. And that's not a good attitude to have in team-based content.