Synesthesia is quite common with ASDs and it doesn't necessarily mean that you have to see colours with numbers/ letters. That particular thing is known as "grapheme-colour synesthesia" and it is only one of the various types. People with synesthesia may have only one type of synesthesia very strongly, or a combination, or many of them not as strongly, etc. It varies greatly. I would guess that your thinking in shapes in connection to feelings is a form of synesthesia. As you become aware of synesthesia, you may start noticing other instances of it in your life. Even if you don't, what you already do qualifies in my opinion.
I have almost every type you can imagine but they are not so strong that they invade my life to the point where they are distracting. I'll share what I have:
I see colours for strong emotions (hot pink with a glowing golden centre and flecks of neon green for very intense romantic love).
I have grapheme-colour synesthesia (the numbers and letters with colours, also certain whole words, like names - usually based on their first letter).
I also have spacial sequence synesthesia (also perhaps known as "number-form synesthesia"), which means picturing numbers laid out in a certain spacial sequence. In my case they start like a graph, with 0 at "ground level" and then slowly rising indefinitely. The interesting thing is that the rise of the numbers isn't perfectly even, so some parts of the never-ending "hill" of the graph seem to rise more steeply depending on which numbers are there (i.e. after 100). As a kid, I used to see it as a snowy ski-slope, since I did some cross-country skiing, but as I matured it became a green graph on a black outer space background.
I have sound-colour synesthesia, so I picture all music as various shapes and washes of colours.. pretty much any combination of shapes and colours you could think of. Normally, they don't invade my vision, but I've had a couple VERY intense ones when listening to music while starting to fall asleep.
Here's an interesting one: personification. I do this almost exclusively with numbers 1-9. Each one has a distinct personality and gender. For instance, they are all either male or female except for 2 which is androgynous, number 8 is kind of a bully, and 9 is a bit haughty, etc. I had these thoughts very strongly as an elementary-school aged child, and I would think of their personalities and interactions while doing math problems.. which led to major distraction!
Lastly: lexical-gustatory synesthesia. This is associating certain words with tastes. I only have it very rarely. I also occasionally associate a colour with a very distinct flavour, such as a certain light yellow to synthetic banana flavour.