1.5yo and constipation

DD2 is 19 months and is constipated. She has had this on and off since birth and also experiences bleeding with it. She is a terrible eater and always has been. I've been to the "feeding clinic" about it, aka a speech therapist, and they've said I need to be patient and hopefully she will grow out of it. She originally didn't like to touch any wet foods but was happy to eat them off a spoon so she is really still eating very much 10month type foods, blended to chunks. She doesn't eat fruit unless it's fruit puree, would eat grated or stick cheese for all 3 meals a day if she could, it's about the only thing she loves. Will eat yoghurt. I can get her to eat casseroles etc that I blend lightly with rice or cook with rissoni or macaroni, and has now finally started to actually eat and swollen some chicken breast nuggets but only 2 or 3 very small pieces, oh and hot chips she will sometimes eat also. There are a few toddler fruit bars she will chew on, but again alot of it is just chewing or biting and not actually swolling it. She is always given two dinners (one that I know she may eat although that is dependent on what mood she is in and will often shake her head for "no" and turn her head away, or swat the spoon away) and then she is also given some of the dinner the rest of the family is eating. Sometimes she might try a few pieces or have a couple spoon fulls herself but mostly she just plays with it and throws it on the floor. Obviously her terrible eating is affecting her digestive system and hence the constipation.

I'm struggling to help with the constipation and she has been quite bad the last few weeks and seems to be causing her tummy pain and obviously a sore bottom. I know milk wouldn't be helping it but at the moment, with her eating patterns, milk is really what is giving her some calories and I was told to keep up her bottles.

She regresses with her eating when she has teeth movement (she has molars doing their final movement out of the gum), and also has this happen if she gets sick. She will regress to only eating puree fruit & yoghurt and pretty much nothing else. She completely goes off eating any hot foods.

Can i give her anything to help keep her regular? I've given coloxyl and infants friend tonight to start and try to loosen her up and help her bottom heal but not sure due to her age what else i can give her to help keep her more regular as an ongoing approach.

I think a trip to the GP might be in order but thought I'd ask for some suggestions here also.

Also open to any suggestions on the eating issues also if anyone has had similar experience (it's so frustrating as my DD1 is complete opposite, I have to tell her she has had enough to eat, I have no idea where she puts it all)..